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Previous studies on the granular layer of the cerebellar cortex have revealed a wide distribution of different subpopulations of less-known large neuron types, called “non-traditional large neurons”, which are distributed in three different zones of the granular layer. These neuron types are mainly involved in the formation of intrinsiccircuits inside the cerebellar cortex. A subpopulation of these neuron types is represented by the synarmotic neuron, which could play a projective role within the cerebellar circuitry. The synarmotic neuron cell body map within the internal zone of the granular layer or in the subjacent white substance. Furthermore, the axon crosses the granular layer and runs in the subcortical white substance, to reenter in an adjacent granular layer, associating two cortico-cerebellar regions of the same folium or of different folia, or could project to the intrinsic cerebellar nuclei. Therefore, along with the Purkinje neuron, the traditional projective neuron type of the cerebellar cortex, the synarmotic neuron is candidate to represent the second projective neuron type of the cerebellar cortex. Studies of chemical neuroanatomy evidenced a predominant inhibitory GABAergic nature of the synarmotic neuron, suggesting that it may mediate an inhibitory GABAergic output of cerebellar cortex within cortico-cortical interconnections or in projections towards intrinsic cerebellar nuclei. On this basis, the present minireview mainly focuses on the morphofunctional and neurochemical data of the synarmotic neuron, and explores its potential involvement in some forms of cerebellar ataxias.

The existence of multiple pairs of smooth positive solutions for a Carrier problem, driven by a p(x)-Laplacian operator, is studied. The approach adopted combines sub-super solutions, truncation, and variational techniques. In particular, after an explicit computation of a sub-solution, obtained combining a monotonicity type hypothesis on the reaction term and the Giacomoni–Takáč’s version of the celebrated Díaz–Saá’s inequality, we derive a multiplicity of solution by investigating an associated one-dimensional fixed point problem. The nonlocal term involved may be a sign-changing function and permit us to obtain the existence of multiple pairs of positive solutions, one for each “positive bump” of the nonlocal term. A new result, also for a constant exponent, is established and an illustrative example is proposed.

Existence of two solutions to a parametric singular quasi-linear elliptic problem is proved. The equation is driven by the Φ\Phi -Laplacian operator, and the reaction term can be nonmonotone. The main tools employed are the local minimum theorem and the Mountain pass theorem, together with the truncation technique. Global C1,τ{C}^{1,\tau } regularity of solutions is also investigated, chiefly via a priori estimates and perturbation techniques.

A short account of some recent existence, multiplicity, and uniqueness results for singular p-Laplacian problems either in bounded domains or in the whole space is performed, with a special attention to the case of convective reactions. An extensive bibliography is also provided.

Screening for early symptoms of cognitive impairment enables timely interventions for patients and their families. Despite the advances in dementia diagnosis, the current nosography of neurocognitive disorders (NCDs) seems to overlook some clinical manifestations and predictors that could contribute to understanding the conversion from an asymptomatic stage to a very mild one, eventually leading to obvious disease. The present review examines different diagnostic approaches in view of neurophysiological and neuropsychological evidence of NCD progression, which may be subdivided into: (1) preclinical stage; (2) transitional stage; (3) prodromal or mild stage; (4) major NCD. The absence of univocal criteria and the adoption of ambiguous or narrow labels might complicate the diagnostic process. In particular, it should be noted that: (1) only neuropathological hallmarks characterize preclinical NCD; (2) transitional NCD must be assessed through proactive neuropsychological protocols; (3) prodromal/mild NCDs are based on cognitive functional indicators; (4) major NCD requires well-established tools to evaluate its severity stage; (5) insight should be accounted for by both patient and informants. Therefore, the examination of evolving epidemiological and clinical features occurring at each NCD stage may orient primary and secondary care, allowing for more targeted prevention, diagnosis, and/or treatment of both cognitive and functional impairment.

We consider a nonlinear boundary value problem with degenerate nonlocal term depending on the Lq-norm of the solution and the p-Laplace operator. We prove the multiplicity of positive solutions for the problem, where the number of solutions doubles the number of “positive bumps” of the degenerate term. The solutions are also ordered according to their Lq-norms.

The existence and the multiplicity of periodic solutions for a parameter dependent second order Hamiltonian system are established via linking theorems. A monotonicity trick is adopted in order to prove the existence of an open interval of parameters for which the problem under consideration admits at least two non trivial qualified solutions.

Infinitely many solutions for a nonlinear sixth-order differential equation are obtained. The variational methods are adopted and an oscillating behaviour on the nonlinear term is required, avoiding any symmetry assumption.

The paper sets forth a new type of variational problem without any ellipticity or monotonicity condition. A prototype is a differential inclusion whose driving operator is the competing weighted $(p,q)$-Laplacian $-\Delta_p u+\mu\Delta_q u$ with $\mu\in \mathbb{R}$. Local and nonlocal boundary value problems fitting into this nonstandard setting are examined.

Phytochemicals from plant foods are considered essential to human health. Known for their role in the adaptation of plants to their environment, these compounds can induce adaptive responses in cells, many of which are directed at maintaining the redox tone. Indicaxanthin is a long-known betalain pigment found in the genus Opuntia of cactus pear and highly concentrated in the edible fruits of O. ficus indica, L. whose bioactivity has been overlooked until recently. This review summarizes studies conducted so far in vitro and in vivo, most of which have been performed in our laboratory. The chemical and physicochemical characteristics of Indicaxanthin are reflected in the molecule’s reducing properties and antioxidant effects and help explain its ability to interact with membranes, modulate redox-regulated cellular pathways, and possibly bind to protein molecules. Measurement of bioavailability in volunteers has been key to exploring its bioactivity; amounts consistent with dietary intake, or plasma concentration after dietary consumption of cactus pear fruit, have been used in experimental setups mimicking physiological or pathophysiological conditions, in cells and in animals, finally suggesting pharmacological potential and relevance of Indicaxanthin as a nutraceutical. In reporting experimental results, this review also aimed to raise questions and seek insights for further basic research and health promotion applications.

In the central nervous system (CNS), dopamine (DA) is involved in motor and cognitive functions. Although the cerebellum is not been considered an elective dopaminergic region, studies attributed to it a critical role in dopamine deficit-related neurological and psychiatric disorders [e.g., Parkinson's disease (PD) and schizophrenia (SCZ)]. Data on the cerebellar dopaminergic neuronal system are still lacking. Nevertheless, biochemical studies detected in the mammalians cerebellum high dopamine levels, while chemical neuroanatomy studies revealed the presence of midbrain dopaminergic afferents to the cerebellum as well as wide distribution of the dopaminergic receptor subtypes (DRD1-DRD5). The present review summarizes the data on the cerebellar dopaminergic system including its involvement in associative and projective circuits. Furthermore, this study also briefly discusses the role of the cerebellar dopaminergic system in some neurologic and psychiatric disorders and suggests its potential involvement as a target in pharmacologic and non-pharmacologic treatments.

Background The aim of this study was to investigate if the supplementation with Opuntia ficus-indica (OFI) juice may affect plasma redox balance and heart rate variability (HRV) parameters following a maximal effort test, in young physically active women. Methods A randomized, double blind, placebo controlled and crossover study comprising eight women (23.25 ± 2.95 years, 54.13 ± 9.05 kg, 157.75 ± 0.66 cm and BMI of 21.69 ± 0.66 kg/m2) was carried out. A juice containing OFI diluted in water and a Placebo solution were supplied (170 ml; OFI = 50 ml of OFI juice + 120 ml of water; Placebo = 170 ml beverage without Vitamin C and indicaxanthin). Participants consumed the OFI juice or Placebo beverage every day for 3 days, before performing a maximal cycle ergometer test, and for 2 consecutive days after the test. Plasma hydroperoxides and total antioxidant capacity (PAT), Skin Carotenoid Score (SCS) and HRV variables (LF, HF, LF/HF and rMSSD) were recorded at different time points. Results The OFI group showed significantly lower levels of hydroperoxides compared to the Placebo group in pre-test, post-test and 48-h post-test. PAT values of the OFI group significantly increased compared to those of the Placebo group in pre-test and 48-h post-test. SCS did not differ between groups. LF was significantly lower in the OFI group 24-h after the end of the test, whereas rMSSD was significantly higher in the OFI group 48-h post-test. Conclusion OFI supplementation decreased the oxidative stress induced by intense exercise and improved autonomic balance in physically active women.

Background: Dietary ingredients and food components are major modifiable factors protecting immune system and preventing the progression of a low-grade chronic inflammation responsible for age-related diseases. Objective: Our study explored whether cactus pear (Opuntia ficus-indica, Surfarina cultivar) fruit supplementation modulates plasma inflammatory biomarkers in healthy adults. Correlations between inflammatory parameters and antioxidant status were also assessed in parallel. Design: In a randomised, 2-period (2 weeks/period), crossover, controlled-feeding study, conducted in 28 healthy volunteers [mean age 39.96 (±9.15) years, BMI 23.1 (±1.5) kg/m2], the effects of a diet supplemented with cactus pear fruit pulp (200 g, twice a day) were compared with those of an equivalent diet with isocaloric fresh fruit substitution. Results: With respect to control, cactus pear diet decreased ( p < 0.05) the pro-inflammatory markers such as tumour necrosis factor-α (TNF-α), interleukin (IL)-1β, interferon-γ (INF)-γ, IL-8, C-reactive protein (CRP) and erythrocyte sedimentation rate (ESR), whereas it increased ( p < 0.05) the anti-inflammatory marker IL-10. Moreover, the diet decreased ratios between pro-inflammatory biomarkers (CRP, IL-6, IL-8, TNF-α) and anti-inflammatory biomarker (IL-10) ( p < 0.05). Cactus pear supplementation caused an increase ( p < 0.05) in dermal carotenoids (skin carotenoid score, SCS), a biomarker of the body antioxidant status, with correlations between SCS and CRP (r = −0.905, p < 0.0001), IL-8 (r = −0.835, p < 0.0001) and IL-10 (r = 0.889, p < 0.0001). Conclusions: The presently observed modulation of both inflammatory markers and antioxidant balance suggests cactus pear fruit as a novel and beneficial component to be incorporated into current healthy dietary habits.

The existence and the multiplicity of periodic solutions for a parameter dependent second order Hamiltonian system are established via linking theorems. A monotonicity trick is adopted in order to prove the existence of an open interval of parameters for which the problem under consideration admits at least two non trivial qualified solutions.

Manna is produced from the spontaneous solidification of the sap of some Fraxinus species, and, owing its content in mannitol, is used in medicine as a mild laxative. Manna is also a rich source of characteristic bio-phenols with reducing, antioxidant and anti-inflammatory properties. This study assesses the activity of a hydrophilic extract of manna (HME) on cellular and molecular events in human colon-rectal cancer cells. HME showed a time- and concentration-dependent anti-proliferative activity, measured by MTT assay, in all the cell lines examined, namely Caco-2, HCT-116 and HT-29. The amounts of HME that caused 50% of cell death after a 24 h treatment were 8.51 ± 0.77, 10.73 ± 1.22 and 28.92 ± 1.99 mg manna equivalents/mL, respectively; no toxicity was observed in normally differentiated Caco-2 intestinal cells. Hydroxytyrosol, a component of HME known for its cytotoxic effects on colon cancer cells, was ineffective, at least at the concentration occurring in the extract. Through flow-cytometric techniques and Western blot analysis, we show that HME treatment causes apoptosis, assessed by phosphatidylserine exposure, as well as a loss of mitochondrial membrane potential, an intracellular formation of reactive oxygen species (ROS), increases in the levels of cleaved PARP-1, caspase 3 and Bax, and a decrease in Bcl-2 expression. Moreover, HME interferes with cell cycle progression, with a block at the G1/S transition. In conclusion, the phytocomplex extracted from manna exerts an anti-proliferative activity on human colon cancer cells through the activation of mitochondrial pathway-mediated apoptosis and cell cycle arrest. Our data may suggest that manna could have the potential to exert chemo-preventive effects for the intestine.

Combining phytochemicals with chemotherapics is an emerging strategy to treat cancer to overcome drug toxicity and resistance with natural compounds. We assessed the effects of indicaxanthin (Ind), a pigment obtained from Opuntia ficus-indica (L. Mill) fruit, combined with cisplatin (CDDP) against cervical cancer cells (HeLa). Measured cell viability via Trypan blue assay; cell morphology via fluorescence microscopy; apoptosis, cell cycle, mitochondrial membrane potential (MMP) and cell redox balance via flow-cytometry; expression levels of apoptosis-related proteins via western blot. Cell viability assays and Chou-Talalay plot demonstrated that the combination of CDDP and Ind had synergistic cytotoxic effects. Combined treatment had significant effects (p < 0.05) on phosphatidylserine externalization, cell morphological changes, cell cycle arrest, fall in MMP, ROS production and GSH decay compared with the individual treatment groups. Bax, cytochrome c, p53 and p21waf1 were over-expressed, while Bcl-2 was downregulated. Pre-treatment with N-acetyl-l-cysteine abolished the observed synergistic effects. We also demonstrated potentiation of CDDP anticancer activity by nutritionally relevant concentrations of Ind. Oxidative stress-dependent mitochondrial cell death is the basis of the chemosensitizing effect of Ind combined with CDDP against HeLa cancer cells. ROS act as upstream signaling molecules to initiate apoptosis via p53/p21waf1 axis. Ind can be a phytochemical of interest in combo-therapy.

Background: Eryptosis is a physiological, apoptosis-like death of injured erythrocytes crucial to prevent premature haemolysis and the pathological sequalae generated by cell-free haemoglobin. When dysregulated, the process is associated to several inflammatory-based pathologies. 4-Hydroxy-trans-2-nonenal (HNE) is an endogenous signalling molecule at physiological levels and, at higher concentrations, is involved in the pathogenesis of several inflammatory-based diseases. This work evaluated whether HNE could induce eryptosis in human erythrocytes. Methods: Measurements of phosphatidylserine, cell volume, intracellular oxidants, Ca++, glutathione, ICAM-1, and ceramide were assessed by flow cytometry. Scanning electron microscopy evaluated morphological alterations of erythrocytes. Western blotting assessed caspases. PGE2 was measured by ELISA. Adhesion of erythrocytes on endothelial cells was evaluated by gravity adherence assay. Results: HNE in the concentration range between 10–100 µM induces eryptosis, morphological alterations correlated to caspase-3 activation, and increased Ca++ levels. The process is not mediated by redox-dependent mechanisms; rather, it strongly depends on PGE2 and ceramide. Interestingly, HNE induces significant increase of erythrocytes adhesion to endothelial cells (ECs) that are in turn dysfunctionated as evident by overexpression of ICAM-1. Conclusions: Our results unveil a new physiopathological role for HNE, provide mechanistic details of the HNE-induced eryptosis, and suggest a novel mechanism through which HNE could exert pro-inflammatory effects.

Manna, a very singular vegetable product derived from the spontaneous solidification of the sap of some Fraxinus species, has long been known for its mild laxative and emollient properties. In this work, a hydro-alcoholic extract of manna (HME) from Sicilian Fraxinus angustifolia Vahl was investigated using HPLC-DAD to find phenol components and using chemical and biological in vitro assays to determine its reducing, antioxidant and anti-inflammatory capacity. We identified elenolic acid, tyrosol, hydroxytyrosol, catechin, fraxetin, verbascoside, gallic acid, procyanidin-B1, and luteolin 3,7 glucoside, in order of abundance. Measurements of total antioxidant activity by Folin-Ciocalteu reaction and ferric reducing ability (FRAP), as well as of scavenger activity towards ABTS•+, DPPH•, and perferryl-myoglobin radicals, showed that the phytocomplex effectively reduced oxidants with different standard potentials. When compared with vitamin E, HME also behaved as an efficient chain-breaking antioxidant against lipoperoxyl radicals from methyl linoleate. In cellular models for oxidative stress, HME counteracted membrane lipid oxidation of human erythrocytes stimulated by tert-butyl hydroperoxide and prevented the generation of reactive oxygen species, as well as the GSH decay in IL-1β−activated intestinal normal-like cells. Moreover, in this in vitro intestinal bowel disease model, HME reduced the release of the pro-inflammatory cytokines IL-6 and IL-8. These findings may suggest that manna acts as an antioxidant and anti-inflammatory natural product in humans, beyond its well-known effects against constipation.

Several studies have recently investigated the role of nutraceuticals in complex pathophysiological processes such as oxidative damages, inflammatory conditions and excitotoxicity. In this regard, the effects of nutraceuticals on basic functions of neuronal cells, such as excitability, are still poorly investigated. For this reason, the possible modulation of neuronal excitability by phytochemicals (PhC) could represent an interesting field of research given that excitotoxicity phenomena are involved in neurodegenerative alterations leading, for example, to Alzheimer’s disease. The present study was focused on indicaxanthin from Opuntia ficus indica, a bioactive betalain pigment, with a proven antioxidant and anti-inflammatory potential, previously found to cross blood-brain barrier (BBB) and to modulate the bioelectric activity of hippocampal neurons. On this basis, we aimed at detecting the specific brain areas where indicaxanthin localizes after oral administration at dietary-achievable amounts and highlighting eventual local effects on the excitability of single neuronal units. HPLC analysis of brain tissue 1 h after ingestion of 2 μmol/kg indicaxanthin indicated that the phytochemical accumulates in cortex, hippocampus, diencephalon, brainstem and cerebellum, but not in the striato-pallidal complex. Then, electrophysiological recordings, applying the microiontophoretic technique, were carried out with different amounts of indicaxanthin (0.34, 0.17, 0.085 ng/neuron) to assess whether indicaxanthin influenced the neuronal firing rate. The data showed that the bioelectric activity of neurons belonging to different brain areas was modulated after local injection of indicaxanthin, mainly with dose-related responses. A predominating inhibitory effect was observed, suggesting a possible novel beneficial effect of indicaxanthin in reducing cell excitability. These findings can constitute a new rationale for exploring biological mechanisms through which PhC could modulate neuronal function with a relapse on complex cognitive brain process and related neurodegenerative conditions.

We consider a nonlinear parametric Neumann problem driven by a nonhomogeneous differential operator with a reaction which is $(p-1)$-superlinear near $\pm\infty$ and exhibits concave terms near zero. We show that for all small values of the parameter, the problem has at least five solutions, four of constant sign and the fifth nodal. We also show the existence of extremal constant sign solutions.

A new series of nortopsentin analogues, in which the imidazole ring of the natural product was replaced by thiazole and the indole unit bound to position 2 of the thiazole ring was substituted by a 7-azaindole moiety, was efficiently synthesized. Two of the new nortopsentin analogues showed good antiproliferative effect against the totality of the NCI full panel of human tumor cell lines (~60) having GI50 values ranging from low micromolar to nanomolar level. The mechanism of the antiproliferative effect of these derivatives, investigated on human hepatoma HepG2 cells, was pro-apoptotic, being associated with externalization of plasma membrane phosphatidylserine and mitochondrial dysfunction. Moreover, the compounds induced a concentration-dependent accumulation of cells in the subG0/G1phase, while confined viable cells in G2/M phase.

β-cryptoxanthin (β-Cx) and phytosterols (Ps) have potential against different cancer types, including colon cancer. However, their combined action has not been reported so far. Human colon cancer Caco-2 cells were treated 24 h with β-Cx and/or main dietary Ps (β-sitosterol, campesterol and stigmasterol), alone or in combination, at concentrations compatible with physiological human serum levels. A decrease in cell viability due to apoptosis (rise in sub-G1 population and exposure of membrane phosphatidylserine) was accompanied with dephosphorylation of BAD, mitochondrial depolarization and caspase 3-dependent PARP cleavage, with intracellular Ca2+ influx and increase of RONS levels as initial triggers. Ps and β-Cx, alone or in combination showed anti-proliferative activity against human colon adenocarcinoma Caco-2 cells through the mitochondrial pathway of apoptosis. No additive or synergistic effects were observed. The importance of bioactivity-guided assays with mixtures of dietary bioactive compounds to determine their eventual interactions in the functional food context is demonstrated.

Two new series of nortopsentin analogues, in which the imidazole ring of the natural product was replaced by thiazole and indole units were both substituted by 7-azaindole moieties or one indole unit was replaced by a 6-azaindole portion, were efficiently synthesized. Compounds belonging to both series inhibited the growth of HCT-116 colorectal cancer cells at low micromolar concentrations, whereas they did not affect the viability of normal-like intestinal cells. A compound of the former series induced apoptosis, evident as externalization of plasma membrane phosphatidylserine (PS), and changes of mitochondrial trans-membrane potential, while blocking the cell cycle in G2/M phase. In contrast, a derivative of the latter series elicited distinct responses in accordance with the dose. Thus, low concentrations (GI30) induced morphological changes characteristic of autophagic death with massive formation of cytoplasmic acid vacuoles without apparent loss of nuclear material, and with arrest of cell cycle at the G1 phase, whereas higher concentrations (GI70) induced apoptosis with arrest of cell cycle at the G1 phase.

Background/Aims: Oxysterol activity on the erythrocyte (RBC) programmed cell death (eryptosis) had not been studied yet. Effects of an oxysterol mixture in hyper-cholesterolemic-relevant proportion, and of individual compounds, were investigated on RBCs from healthy humans. Methods: Membrane phosphatidylserine (PS) externalization, calcium entry, ROS production, amino-phospholipid translocase (APLT) activity were evaluated by cytofluorimetric assays, cell volume from forward scatter. Prostaglandin PGE2 was measured by ELISA; GSH-adducts and lipoperoxides by spectrophotometry. Involvement of protein kinase C and caspase was investigated by inhibitors staurosporin, calphostin C, and Z-DEVD-FMK, respectively. Results: Oxysterols caused PS externalization and cell shrinkage, associated with PGE2release, opening of PGE2-dependent calcium channels, ROS production, GSH depletion, membrane lipid oxidation. Addition of antioxidants prevented Ca2+ influx and eryptosis. Calcium removal prevented cell shrinkage, with small effect (-20%) on the PS exposure, whereas ROS generation was unaltered. Either in the presence or absence of calcium i) oxysterols inhibited APLT, ii) staurosporin, calphostin C, Z-DEVD-FMK blunted and iii) antioxidants fully prevented the oxysterol-induced PS externalization. Only 7-ketocholesterol and cholestan-3β,5α,6β-triol were individually active. Eryptosis was observed in RBCs isolated after ex vivo spiking of human whole blood with the oxysterol mixture. Conclusions: Oxysterols induce an oxidative stress-dependent eryptosis, involving calcium-independent mechanisms. Eryptotic activity of oxysterols may be relevant in vivo.

Macrophages come across active prostaglandin (PG) metabolism during inflammation, shunting early production of pro-inflammatory towards anti-inflammatory mediators terminating the process. This work for the first time provides evidence that a phytochemical may modulate the arachidonate (AA) metabolism in lipopolysaccharide (LPS)-stimulated RAW 264.7 macrophages, promoting the ultimate formation of anti-inflammatory cyclopentenone 15deoxy-PGJ2. Added 1 h before LPS, indicaxanthin from Opuntia Ficus Indica prevented activation of nuclear factor-κB (NF-κB) and over-expression of PGE2 synthase-1 (mPGES-1), but up-regulated cyclo-oxygenase-2 (COX-2) and PGD2 synthase (H-PGDS), with final production of the anti-inflammatory cyclopentenone. The effects were positively related with concentration between 50 and 100 µM. Indicaxanthin did not have any effect in the absence of LPS. A kinetic study investigating the redox status of LPS-stimulated macrophages between 0.5 and 12 h, either in the absence or in the presence of 50–100 µM indicaxanthin, revealed a differential control of ROS production, with early (0.5–3 h) modest inhibition, followed by a progressive (3–12 h) concentration-dependent enhancement over the level induced by LPS alone. In addition, indicaxanthin caused early (0.5–3 h) concentration-dependent elevation of conjugated diene lipid hydroperoxides, and production of hydroxynonenal-protein adducts, over the amount induced by LPS. In LPS-stimulated macrophages indicaxanthin did not affect PG metabolism when co-incubated with either an inhibitor of NADPH oxidase or vitamin E. It is concluded that LPS-induced pro-oxidant activity of indicaxanthin at the membrane level allows formation of signaling intermediates whose accumulation modulates PG biosynthetic pathway in inflamed macrophages.

Thirty samples from thirteen Sicilian monofloral honeys by the local black honeybee, and two honeydew honeys, were studied to assess phenol content, reducing power and antioxidant capacity as well as correlations among these parameters. Honeys from Apiaceae showed the highest phenol amount and capacity to reduce ferric ion and stable chemical radicals, whereas honeys from Leguminosae the lowest. All honeys were active against myoglobin-derived radicals usually formed in red meat after storage and/or heating and significant correlation (p = 0.023) was found between flavonoid content and deactivation rate of this radical. Dill > almond > tangerine > thistle > sulla honeys inhibited formation of lipoperoxides in either iron/ascorbate or azoinitiator -induced membrane lipid oxidation, whereas eucalyptus honey was mostly effective in the metal-dependent model. Honeys by black honeybee possess remarkable reducing power and antioxidant potential against radicals of interest in dietary foodstuffs.

In this paper we present some recent multiplicity results for a class of second order Hamiltonian systems. Exploiting the variational structure of the problem, it will be shown how the existence of multiple, even infinitely many, periodic solutions can be assured.

Multiplicity results for an eigenvalue second-order Hamiltonian system are investigated. Using suitable critical points arguments, the existence of an exactly determined open interval of positive eigenvalues for which the system admits at least three distinct periodic solutions is established. Moreover, when the energy functional related to the Hamiltonian system is not coercive, an existence result of two distinct periodic solutions is given.