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Blinatumomab is a bispecific anti-CD3 and anti-CD19 antibody that acts as a T-cell engager: by binding CD19+ lymphoblasts, blinatumomab recruits cytotoxic CD3+ T-lymphocytes to target the cancer cells. Here we describe seven different patients affected by B-cell precursor acute lymphoblastic leukemia (Bcp-ALL) and treated with blinatumomab, on which we evaluated the potential association between the amount of different T-cells subsets and deep molecular response after the first cycle, identified as a complete remission in the absence of minimal residual disease (CR/MRD). The immune-system effector cells studied were CD3+, CD4+ effector memory (T4-EM), CD8+ effector memory (T8-EM), and T-regulatory (T-reg) lymphocytes, and myeloid-derived suppressor cells (MDSC). Measurements were performed in the peripheral blood using flow cytometry of the peripheral blood at baseline and after the first cycle of blinatumomab. The first results show that patients with a higher proportion of baseline T-lymphocytes achieved MRD negativity more frequently with no statistically significant difference (p=0.06) and without differences in the subpopulation count following the first treatment. These extremely preliminary data could potentially pave the way for future studies, including larger and less heterogeneous cohorts, in order to assess the T-cell kinetics in a specific set of patients with potential synergy effects in targeting myeloid-derived suppressor cells (MDSC), commonly known to have an immune evasion mechanism in Bcp-ALL.

Abstract Aggressive SM + AML has limited therapeutic options. Even a strong combination of decitabine–venetoclax–midostaurin has a transient effect on AML and a mitigated effect on SM. Larger series are required to identify the best therapeutic strategy.

We consider the Dirichlet problem \begin{equation*} - \Delta^{K_p}_{p(x)} u(x) - \Delta^{K_q}_{q(x)} u(x) = f(x,u(x), \nabla u(x)) \quad \mbox{in }\Omega, \quad u\big{|}_{\partial \Omega}=0, \end{equation*} driven by the sum of a $p(x)$-Laplacian operator and of a $q(x)$-Laplacian operator, both of them weighted by indefinite (sign-changing) Kirchhoff type terms. We establish the existence of weak solution and strong generalized solution, using topological tools (properties of Galerkin basis and of Nemitsky map). In the particular case of a positive Kirchhoff term, we obtain the existence of weak solution ($=$ strong generalized solution), using the properties of pseudomonotone operators.

Abstract We are concerned with the existence and nonexistence of global weak solutions for a certain class of time-fractional inhomogeneous pseudo-parabolic-type equations involving a nonlinearity of the form | u | p + ι | ∇ u | q $|u|^{p}+\iota |\nabla u|^{q}$ , where p , q > 1 $p,q>1$ , and ι ≥ 0 $\iota \geq 0$ is a constant. The cases ι = 0 $\iota =0$ and ι > 0 $\iota >0$ are discussed separately. For each case, the critical exponent in the Fujita sense is obtained. We point out two interesting phenomena. First, the obtained critical exponents are independent of the fractional orders of the time derivative. Secondly, in the case ι > 0 $\iota >0$ , we show that the gradient term induces a discontinuity phenomenon of the critical exponent.

Mathematics represents a wide area of knowledge and is an essential subject in many technologies and applications [...]

Infections occurring in immunocompromised patients after intensive chemotherapy are often difficult to eradicate and are capable of even being fatal. New emergent and dangerous drug-resistant micro-organisms are likely to appear in these specific scenarios. Clinical features mainly include progressive pneumonia, bacteriemia/fungemia, or extrapulmonary dissemination among infections. The treatment of these microorganisms is still an open challenge since there is a lack of clear treatment guidelines. Indeed, infections from these microorganisms can lead to a rapidly fatal clinical course in immunocompromised patients, especially those who have acute leukemia. We describe the case of a young patient with acute myeloid leukemia who contracted an infection from Saprochaete capitata during post-chemotherapy aplasia.

We study the behavior of solutions for the parametric equation $ -\Delta_{p}^{a_1} u(z)-\Delta_{q}^{a_2} u(z) = \lambda |u(z)|^{q-2} u(z)+f(z,u(z)) \quad \mbox{in } \Omega,\, \lambda >0, $ under Dirichlet condition, where $ \Omega \subseteq \mathbb{R}^N $ is a bounded domain with a $ C^2 $-boundary $ \partial \Omega $, $ a_1, a_2 \in L^\infty(\Omega) $ with $ a_1(z), a_2(z) > 0 $ for a.a. $ z \in \Omega $, $ p, q \in (1, \infty) $ and $ \Delta_{p}^{a_1}, \Delta_{q}^{a_2} $ are weighted versions of $ p $-Laplacian and $ q $-Laplacian. We prove existence and nonexistence of nontrivial solutions, when $ f(z, x) $ asymptotically as $ x \to \pm \infty $ can be resonant. In the studied cases, we adopt a variational approach and use truncation and comparison techniques. When $ \lambda $ is large, we establish the existence of at least three nontrivial smooth solutions with sign information and ordered. Moreover, the critical parameter value is determined in terms of the spectrum of one of the differential operators.

Patients affected by myelofibrosis (MF) or polycythemia vera (PV) and treated with ruxolitinib are at high risk for severe coronavirus disease 2019. Now a vaccine against the virus SARS-CoV-2, which is responsible for this disease, is available. However, sensitivity to vaccines is usually lower in these patients. Moreover, fragile patients were not included in large trials investigating the efficacy of vaccines. Thus, little is known about the efficacy of this approach in this group of patients. In this prospective single-center study, we evaluated 43 patients (30 MF patients and 13 with PV) receiving ruxolitinib as a treatment for their myeloproliferative disease. We measured anti-spike and anti-nucleocapsid IgG against SARS-CoV2 15-30 days after the second and the third BNT162b2 mRNA vaccine booster dose. Patients receiving ruxolitinib showed an impaired antibody response to complete vaccination (2 doses), as 32.5% of patients did not develop any response. After the third booster dose with Comirnaty, results slightly improved, as 80% of these patients produced antibodies above the threshold positivity. However, the quantity of produced antibodies was well below that reached than those reported for healthy individuals. PV patients elicited a better response than patients affected by MF. Thus, different strategies should be considered for this high-risk group of patients.

This Special Issue of the journal Symmetry is dedicated to recent progress in the field of nonlinear differential problems [...]

Acute myeloid leukemia is a hematological disease with a poor prognosis. Blast cells that characterize the disease are generally present in the bone marrow, but they can sometimes be located in different organs. This rare event can occur at diagnosis or at relapse, together or not with bone marrow involvement, and worsens prognosis and management. Despite this, the introduction into clinical practice of newly approved drugs directed towards molecular targets and approved for acute myeloid leukemia will pave the way for new treatment approaches facing this rare disease. In this paper, we present a case of a patient with acute myeloid leukemia with extramedullary manifestations involving the cutis and responding to FLT3-directed target therapy.

We report a case of a young patient suffering from very-high risk B-acute lymphoblastic leukemia (ALL) refractory to first-line therapy with early central nervous system relapse, sequentially treated with inotuzumab. At this timepoint, the patient showed persistent transfusion-refractory thrombocytopenia (platelets < 5000/uL), fever and cytomegalovirus infection. A bone marrow revaluation showed complete remission of ALL, but hemophagocytic elements and activated macrophages were present. At physical examination, the spleen was palpable. Blood chemistry showed hyperferritinemia (1419 ng/mL, normal range 24–336), NK cells suppression (11 cells/microL, minimum value 90) and IL-6 increase (119.1 pg/dL, normal values < 1.8). Triglycerides and fibrinogen were normal. A diagnosis of hemophagocytic lymphohistiocytosis (HLH) was made according to HLH-2004 criteria. The patient was treated with the IL-1 inhibitor anakinra at escalating dosage. After an initial improvement in altered HLH parameters, a clinical worsening occurred with progressing thrombocytopenia and anemia and a remarkable increase in ferritin (4066 ng/mL). The patient then underwent rituximab-based salvage treatment but died due to HLH and B-ALL progression. HLH could be a rare complication in ALL patients. Despite increasing biological knowledge, prognosis remains poor, and more efforts are needed in order to improve survival in these patients.

A Cauchy viscoelastic problem perturbed by an inverse-square potential, and posed in an exterior domain of RN, is considered under a Dirichlet boundary condition. Using nonlinear capacity estimates specifically adapted to the non-local nature of the problem, the potential function and the boundary condition, we establish sufficient conditions for the nonexistence of weak solutions.

We consider a parametric nonlinear Robin problem driven by the sum of a \(p\)-Laplacian and of a \(q\)-Laplacian (\((p,q)\)-equation). The reaction term is \((p-1)\)-superlinear but need not satisfy the Ambrosetti-Rabinowitz condition. Using variational tools, together with truncation and comparison techniques and critical groups, we show that for all small values of the parameter, the problem has at least five nontrivial smooth solutions, all with sign information.

We consider a parametric Neumann problem driven by a nonlinear nonhomogeneous differential operator plus an indefinite potential term. The reaction term is superlinear but does not satisfy the Ambrosetti-Rabinowitz condition. First we prove a bifurcation-type result describing in a precise way the dependence of the set of positive solutions on the parameter $\lambda>0$. We also show the existence of a smallest positive solution. Similar results hold for the negative solutions and in this case we have a biggest negative solution. Finally using the extremal constant sign solutions we produce a smooth nodal solution.

The potent oral inhibitor of BCL2, venetoclax (VEN), used to treat adults with chronic lymphocytic leukaemia, has been approved in US for the treatment of naïve patients with acute myeloid leukemia (AML) unfit for intensive chemotherapy and recently in Europe, too. However, the drug has been used for years in combination with hypomethylating agents (HMAs) in patients not eligible to other treatment option, according to the so-called off-label use. We collected real-world data about patients treated with VEN + HMAs in the context of a pharmacovigilance project focused on the evaluation of the safety and effectiveness of drugs used for unapproved indication in Italian hospitals. From March to December 2020, 24 patients started treatment with VEN combined with HMAs. 21 patients have been assessed for response. Eleven (52%) patients reached complete remission (CR), and three patients (14%) CR with partial hematological recovery (CRh), with a median duration of response of 4.5 months (range 0.5–12.5). 19 patients experienced at least 1 adverse drug reaction (ADR), mostly serious, including 3 deaths (9% of ADRs; 12.5% of patients) in febrile neutropenia. Hematological toxicities and infections (cytopenia, neutropenia, febrile neutropenia, sepsis), were the most reported ADRs (84.4%). In general, neutropenic fever occurred more frequently in patients treated with decitabine (7 out of 9, 78%) compared to azacitidine (5 out of 15, 33%; p = 0.03), whereas response assessment did not differ based on used HMA (p = 0.1). These results confirm the benefit-risk profile of VEN in a real-world setting of patients with no adequate therapeutic options.

Fungal infections occurring in immunocompromised patients after immuno-chemotherapy treatment, are often difficult to eradicate and capable of even being fatal. Systemic mycoses affecting severely immunocompromised patients often manifest acutely with rapidly progressive pneumonia, fungemia, or manifestations of extrapulmonary dissemination. Opportunistic fungal infections (mycoses) include several pathogens elements, as Candidiasis, Aspergillosis, Mucormycosis (zygomycosis) and Fusariosis. Prompt diagnosis and effective therapy are needed to improve the associated morbidity and mortality, especially in cases with non-canonical fungal localizations and not responsive to the available antifungal drugs.

Mathematical methods are extensively used in dealing with simulation and approximation problems related to computer science, engineering, physics, and many others [...]

We consider a nonlinear nonhomogeneous Robin equation driven by the sum of a \(p\)-Laplacian and of a \(q\)-Laplacian (\((p,q)\)-equation) plus an indefinite potential term and a parametric reaction of logistic type (superdiffusive case). We prove a bifurcation-type result describing the changes in the set of positive solutions as the parameter \(\lambda \gt 0\) varies. Also, we show that for every admissible parameter \(\lambda \gt 0\), the problem admits a smallest positive solution.

We consider a parametric Robin problem driven by a nonlinear, nonhomogeneous differential operator which includes as special cases the p-Laplacian and the (p,q)-Laplacian. The source term is parametric and only locally defined (that is, in a neighborhood of zero). Using suitable cut-off techniques together with variational tools and comparison principles, we show that for all big values of the parameter, the problem has at least three nontrivial smooth solutions, all with sign information (positive, negative and nodal).

In this paper, we consider local Dirichlet problems driven by the (r(u),s(u))-Laplacian operator in the principal part. We prove the existence of nontrivial weak solutions in the case where the variable exponents r,s are real continuous functions and we have dependence on the solution u. The main contributions of this article are obtained in respect of: (i) Carathéodory nonlinearity satisfying standard regularity and polynomial growth assumptions, where in this case, we use geometrical and compactness conditions to establish the existence of the solution to a regularized problem via variational methods and the critical point theory; and (ii) Sobolev nonlinearity, somehow related to the space structure. In this case, we use a priori estimates and asymptotic analysis of regularized auxiliary problems to establish the existence and uniqueness theorems via a fixed-point argument.

We consider a nonlinear Robin problem driven by the p-Laplacian, with unilateral constraints and a reaction term depending also on the gradient (convection term). Using a topological approach based on fixed point theory (the Leray-Schauder alternative principle) and approximating the original problem using the Moreau-Yosida approximations of the subdifferential term, we prove the existence of a smooth solution.

We consider a nonlinear elliptic problem driven by the Dirichlet $p$-Laplacian and a reaction term which depends also on the gradient (convection). No growth condition is imposed on the reaction term $f(z, \cdot,y)$. Using topological tools and the asymptotic analysis of a family of perturbed problems, we prove the existence of a positive smooth solution.

We prove the existence of weak solutions to the Dirichlet boundary value problem for equations involving the $p(x)$-Laplacian-like operator in the principal part, with reaction term satisfying a sub-critical growth condition. We establish the existence of at least one nontrivial weak solution and three weak solutions, by using variational methods and critical point theory.

Higher order fractional differential equations are important tools to deal with precise models of materials with hereditary and memory effects. Moreover, fractional differential inequalities are useful to establish the properties of solutions of different problems in biomathematics and flow phenomena. In the present work, we are concerned with the nonexistence of global solutions to a higher order fractional differential inequality with a nonlinearity involving Caputo fractional derivative. Namely, using nonlinear capacity estimates, we obtain sufficient conditions for which we have no global solutions. The a priori estimates of the structure of solutions are obtained by a precise analysis of the integral form of the inequality with appropriate choice of test function.

We consider a discrete Dirichlet boundary value problem of equations with the (p,q)-Laplacian operator in the principal part and prove the existence of at least two positive solutions. The assumptions on the reaction term ensure that the Euler-Lagrange functional, corresponding to the problem, satisfies an abstract two critical points result.

We study a family of random differential equations with boundary conditions. Using a random fixed point theorem, we prove an existence theorem that yields a unique random solution.

We establish a best proximity pair theorem for noncyclic φ-condensing operators in strictly convex Banach spaces by using a measure of noncompactness. We also obtain a counterpart result for cyclic φ-condensing operators in Banach spaces to guarantee the existence of best proximity points, and so, an extension of Darbo’s fixed point theorem will be concluded. As an application of our results, we study the existence of a global optimal solution for a system of ordinary differential equations.

Abstract We introduce the notion of a modified α-ϕ-fuzzy contractive mapping and prove some results in fuzzy metric spaces for such kind of mappings. The theorems presented provide a generalization of some interesting results in the literature. Two examples and an application to integral equations are given to illustrate the usability of our theory.

We investigate the large time behavior for the inhomogeneous damped wave equation with nonlinear memory ϕtt(t,ω)−Δϕ(t,ω)+ϕt(t,ω)=1Γ(1−ρ)∫0t(t−σ)−ρ|ϕ(σ,ω)|qdσ+μ(ω),t>0, ω∈RN imposing the condition (ϕ(0,ω),ϕt(0,ω))=(ϕ0(ω),ϕ1(ω))inRN, where N≥1, q>1, 0<ρ<1, ϕi∈Lloc1(RN), i=0,1, μ∈Lloc1(RN) and μ≢0. Namely, it is shown that, if ϕ0,ϕ1≥0, μ∈L1(RN) and ∫RNμ(ω)dω>0, then for all q>1, the considered problem has no global weak solution.

This paper is concerned with the nonexistence of global solutions to fractional in time nonlinear Schrödinger equations of the form i α ∂ t α ω ( t , z ) + a 1 ( t ) Δ ω ( t , z ) + i α a 2 ( t ) ω ( t , z ) = ξ | ω ( t , z ) | p , ( t , z ) ∈ ( 0 , ∞ ) × R N , where N ≥ 1 , ξ ∈ C \ { 0 } and p > 1 , under suitable initial data. To establish our nonexistence theorem, we adopt the Pohozaev nonlinear capacity method, and consider the combined effects of absorption and dispersion terms. Further, we discuss in details some special cases of coefficient functions a 1 , a 2 ∈ L l o c 1 ( [ 0 , ∞ ) , R ) , and provide two illustrative examples.

We study the large-time behavior of solutions to the nonlinear exterior problem L u ( t , x ) = κ | u ( t , x ) | p , ( t , x ) ∈ ( 0 , ∞ ) × D c under the nonhomegeneous Neumann boundary condition ∂ u ∂ ν ( t , x ) = λ ( x ) , ( t , x ) ∈ ( 0 , ∞ ) × ∂ D , where L : = i ∂ t + Δ is the Schrödinger operator, D = B ( 0 , 1 ) is the open unit ball in R N , N ≥ 2 , D c = R N ∖ D , p > 1 , κ ∈ C , κ ≠ 0 , λ ∈ L 1 ( ∂ D , C ) is a nontrivial complex valued function, and ∂ ν is the outward unit normal vector on ∂ D , relative to D c . Namely, under a certain condition imposed on ( κ , λ ) , we show that if N ≥ 3 and p < p c , where p c = N N − 2 , then the considered problem admits no global weak solutions. However, if N = 2 , then for all p > 1 , the problem admits no global weak solutions. The proof is based on the test function method introduced by Mitidieri and Pohozaev, and an adequate choice of the test function.

We consider a two-point boundary value problem of second-order random differential equation. Using a variant of the α-ψ-contractive type mapping theorem in metric spaces, we show the existence of at least one solution.

Azacytidine (5-AZA) is the standard first-choice treatment for high-risk myelodysplasia (MDS) patients. However, the clinical outcome for those patients who interrupt treatment or whose disease failed to respond is very poor. In order to identify the cellular pathways that are modified by long-term exposure to 5-AZA, we evaluated key proteins associated with the autophagy pathway by reverse-phase microarray (RPPA). Comparing bone marrow mononucleated cells (BMMCs) obtained from 20 newly-diagnosed patients and after four 5-AZA cycles we found an increased autophagy signaling. We then evaluated ex-vivo the effect of the combination of 5-AZA with autophagy inhibitors chloroquine (CQ) and leupeptin. Since 5-AZA and CQ showed synergism due to an increase of basal autophagy after 5-AZA exposure, we adopted a sequential treatment treating BMMCs with 5 μM 5-AZA for 72 h followed by 10 μM CQ for 24 h and found increased apoptosis, associated to a reduction of G2M phase and increase in G0-G1 phase. Long-term exposure to 5-AZA induced the reduction of the autophagic marker SQSTM1/p62, reversible by CQ or leupeptin exposure. In conclusion, we identified autophagy as a compensatory pathway occurring in MDS-BM after long-term exposure to 5-AZA and we provided evidences that a sequential treatment of 5-AZA followed by CQ could improve 5-AZA efficacy, providing novel insight for tailored therapy in MDS patients progressing after 5-AZA therapy.

We introduce a contractive condition involving new auxiliary function and prove a fixed point theorem for closed multivalued maps on complete metric spaces. An example and an application to integral equation are given in support of our findings.

Recently, Aydi et al. [On fixed point results for α-implicit contractions in quasi-metric spaces and consequences, Nonlinear Anal. Model. Control, 21(1):40–56, 2016] proved some fixed point results involving α-implicit contractive conditions in quasi-b-metric spaces. In this paper we extend and improve these results and derive some new fixed point theorems for implicit contractions in ordered quasi-b-metric spaces. Moreover, some examples and an application to integral equations are given here to illustrate the usability of the obtained results.

The aim of this paper is to introduce generalized F2-Geraghty type fuzzy mappings on a metric space for establishing the existence of fuzzy fixed points of such mappings. As an application of our result, we obtain the existence of common fuzzy fixed point for a generalized F2-Geraghty type fuzzy hybrid pair. These results unify, generalize and complement various known comparable results in the literature. An example and an application to theoretical computer science are presented to support the theory proved herein. Also, to suggest further research on fuzzy mappings, a Feng–Liu type theorem is proved.

We give sufficient conditions for the existence of common fixed points for a pair of mixed multi-valued mappings in the setting of 0-complete partial metric spaces. An example is given to demonstrate the usefulness of our results over the existing results in metric spaces. Finally, we prove a homotopy theorem via fixed point results.

In 2012, Samet et al. introduced the notion of α-ψ-contractive mapping and gave sufficient conditions for the existence of fixed points for this class of mappings. The purpose of our paper is to study the existence of fixed points for multivalued mappings, under an α-ψ-contractive condition of Ćirić type, in the setting of complete b-metric spaces. An application to integral equation is given.

Multivalued mappings and related selection theorems are fundamental tools in many branches of mathematics and applied sciences. In this paper we continue this theory and prove the existence of Caristi type selections for generalized multivalued contractions on complete metric spaces, by using some classes of functions. Also we prove fixed point and quasi-fixed point theorems.