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It is established existence of weak solutions for nonlocal elliptic problems driven by the fractional Laplacian where the nonlinearity is indefinite in sign. More specifically, we shall consider the following nonlocal elliptic problem: (−Δ)su+V(x)u=μa(x)|u|q−2u−λ|u|p−2uinRN,u∈Hs(RN),$$\begin{equation*} {\left\lbrace \def\eqcellsep{&}\begin{array}{rcl}(-\Delta)^s u +V(x)u & = & \mu a(x)|u|^{q-2}u-\lambda |u|^{p-2}u \mbox{ in }\, \mathbf {R}^N, \\[3pt] u\in H^s(\mathbf {R}^N),&&{} \end{array} \right.} \end{equation*}$$where s∈(0,1),s0$\mu , \lambda >0$. The potentials V,a:RN→R$V, a : \mathbf {R}^N \rightarrow \mathbf {R}$ satisfy some extra assumptions. The main feature is to find sharp parameters λ>0$\lambda > 0$ and μ>0$\mu > 0$ where the Nehari method can be applied. In order to do that, we employ the nonlinear Rayleigh quotient together a fine analysis on the fibering maps associated to the energy functional. It is important to mention also that for each parameters λ>0$\lambda > 0$ and μ>0$\mu > 0$, there exist degenerate points in the Nehari set that give serious difficulties. Furthermore, we consider nonlinearities that are superlinear at the origin and superlinear at infinity. In order to overcome these difficulties, we apply some estimates together with a carefully analysis on the fibering maps. Here, we also consider the asymptotic behavior of the weak solutions for our main problem when λ→0$\lambda \rightarrow 0$ or μ→∞$\mu \rightarrow \infty$. Furthermore, we consider a nonexistence result for our main problem under some appropriate conditions on the parameters λ>0$\lambda >0$ and μ>0$\mu > 0$. [ABSTRACT FROM AUTHOR]

It is established existence and multiplicity of solutions for semilinear elliptic problems defined in the whole space R N considering subcritical nonlinearities with some parameters. Here we emphasize that our nonlinearities can be sign-changing functions. The main difficulty is proving the existence of nontrivial solutions by using the Nehari method, taking into account that the Lagrange multipliers theorem cannot be directly applied in our setting. In fact, we consider the case where the fibering map admits inflection points. In other words, we consider the case where the Nehari set admits degenerate critical points. Hence our main contribution is to consider a huge class of semilinear elliptic problems where the standard Nehari method cannot be applied. Using some fine estimates and recovering some compactness results together with the nonlinear Rayleigh quotient, we prove that our main problem admits at least three nontrivial solutions depending on the parameters. [ABSTRACT FROM AUTHOR]

It is established existence, multiplicity, and asymptotic behavior of nonnegative solutions for a quasilinear elliptic problem driven by the Φ -Laplacian operator. One of these solutions is obtained as ground-state solution by applying the well-known Nehari method. The nonlinear term is a concave–convex function which presents a critical behavior at infinity. The concentration-compactness principle is used in order to recover the compactness required in variational methods. [ABSTRACT FROM AUTHOR]

The aim of this study was to evaluate the physiological parameters and thermal comfort indices of commercial layers fed diets containing different levels of vegetable glycerin. A total of 378 Hy-Line White layers at 32 weeks of age were housed in a shed at nine birds per cage. The experiment lasted 84 days. Treatments consisted of a control diet (without glycerin) plus five diets with increasing levels of vegetable glycerin (3, 6, 9, 12, and 15%). The black globe humidity index (BGHI) and radiant heat load (RHL) were out of the thermal comfort zone and were higher in the afternoon period in all production cycles. Respiratory frequency was lower in the morning, when 3% glycerin were added to the diet. The surface temperatures of comb, wattle, back, wings, head, and feet did not differ with the glycerin levels and were higher in the 2nd cycle, but within the range recommended for the species. Glycerin inclusion levels of up to 12% can be used to partially replace corn in diets for layers housed in sheds covered with ceramic tiles without compromising their thermoregulation in a hot environment. [ABSTRACT FROM AUTHOR]

In this paper, the existence and multiplicity of solutions for a quasilinear elliptic problem driven by the -Laplacian operator is established. These solutions are also built as ground state solutions using the Nehari method. The main difficulty arises from the fact that the -Laplacian operator is not homogeneous and the nonlinear term is indefinite. [ABSTRACT FROM AUTHOR]

The aim of this study was to evaluate the effect of protein reduction and supplementation of l-glutamic acid in male broiler diets. A total of 648 chicks of the Cobb 500 strain were distributed in a completely randomized design with six treatments and six replications with eighteen birds per experimental unit. The study comprised pre-starter (1-7 days), starter (8-21 days), growth (22-35 days) and final (36-45 days) phases. The first treatment consisted of a control diet formulated according to the requirements of essential amino acids for each rearing phase. The second and third treatments had crude protein ( CP) reduced by 1.8 and 3.6 percentage points (pp) in relation to the control diet respectively. In the fourth treatment, l-glutamic acid was added to provide the same glutamate level as the control diet, and in the last two treatments, the broilers were supplemented with 1 and 2 pp of glutamate above that of the control diet respectively. The reduction in CP decreased the performance of broilers and the supplementation of l-glutamic acid did not influence performance when supplied in the diets with excess of glutamate. The lowest excreted nitrogen values were observed in the control diet, and treatments 2 and 3, respectively, in comparison with treatments with the use of l-glutamic acid (5 and 6). Retention efficiency of nitrogen was better in the control diet and in the treatment with a reduction of 1.8 pp of CP. It was verified that the serum uric acid level decreased with the CP reduction. A reduction in CP levels of up to 21.3%, 18.8%, 18.32% and 17.57% is recommended in phases from 1 to 7, 8 to 21, 22 to 35 and at 36 to 42 days, respectively, with a level of glutamate at 5.32%, 4.73%, 4.57%, 4.38%, also in these phases. [ABSTRACT FROM AUTHOR]

Sete Cidades is an active central volcano with a summit caldera located in the westernmost part of S. Miguel Island (Azores). Since the settlement of the Island, in the 15th century, many landslide events occurred in this volcano, causing extensive damages in buildings and infrastructures. The study of historical records and the observation of new occurrences showed that landslides in the region have been triggered by heavy rainfall periods, earthquakes and erosion. In order to assess landslide susceptibility at Sete Cidades Volcano, landslide scars and associated deposits were mapped through aerial photographs and field surveys. The obtained data were inserted in a GIS to produce a landslide distribution map. It was concluded that the high density landslide areas are related with (1) major scarp faults, (2) the margin of fluvial channels, (3) the sea cliffs and (4) volcanic landforms, namely the caldera wall. About 73% of the mapped events took place in areas where pyroclastic deposits are the dominant lithology and more than 77% occurred where slopes are equal or higher than 20°. These two parameters were integrated and used to generate a preliminary susceptibility map. The incorporation of vulnerability data into the GIS allowed concluding that 30% of dwellings and most of the roads on Sete Cidades Volcano are located in areas where landslide susceptibility is high to very high. Such conclusion should be taken into account for emergency and land use planning. [ABSTRACT FROM AUTHOR]