Showing papers by "Claudianor O. Alves published in 2022"
10 citations
TL;DR: In this article , a Lions type result for a large class of quasilinear problems on a non-reflexive Orlicz-Sobolev space was proved.
Abstract: In this paper we prove a Lions type result for a large class of Orlicz-Sobolev space that can be nonreflexive and use this result to show the existence of solution for a large class of quasilinear problem on a nonreflexive Orlicz-Sobolev space.
6 citations
TL;DR: In this paper, the existence of a nontrivial solution for the locally Lipschitz function problem was established by employing Variational Methods for Locally Localized Functions (VMLF).
4 citations
TL;DR: In this paper , the existence of global solutions for Dirichlet heat equations involving the 1-Laplacian operator for the Dirichlets problem has been studied and an approximation technique that consists in working with a class of p-laplacians associated with (P) and then taking the limit when p→1+ to get their results.
3 citations
TL;DR: In this paper, a class of variational elliptic problems involving integro-differential diffusion and Dirichlet boundary condition is studied and sign-changing solutions are obtained when the nonlinearity is a sublinear or superlinear power of u +, depending on the size of a positive parameter multiplying the nonlocal term.
2 citations
TL;DR: In this paper , Calcagni, Montobbio and Nardelli studied a class of non-linear equations on Euclidean space building on previous works by the present authors, and proved the existence of (strong) solutions using Schaeffer's fixed point theorem and existence of radial and non-radial strong solutions using the variational approach and the principle of symmetric criticality.
2 citations
2 citations
2 citations
TL;DR: In this article , the existence and concentration of solitary waves for a class of generalized Kadomtsev-Petviashvili equations with the potential in R 2 via the variational methods was studied.
Abstract: A BSTRACT . In this paper, we study the existence and concentration of solitary waves for a class of generalized Kadomtsev-Petviashvili equations with the potential in R 2 via the variational methods.
1 citations
TL;DR: In this article , the authors obtained a nonsmooth version of the infinite-dimensional Fountain Theorem established by Batkam and Colin (2013), where no symmetry condition on the energy functional is needed in their formulation.
Abstract: In this paper, we obtain a nonsmooth version of the infinite-dimensional Fountain Theorem established by Batkam and Colin (2013). No symmetry condition on the energy functional is needed in our formulation. As an application, we prove the existence of multiple solutions for the following class of elliptic system ( S ) Δ u − u ∈ [ f ̲ ( x , u , v ) , f ¯ ( x , u , v ) ] a.e in R N − Δ v + v ∈ [ g ̲ ( x , u , v ) , g ¯ ( x , u , v ) ] a.e in R N , u , v ∈ H 1 ( R N ) , where f and g are measurable functions that satisfy some technical conditions.
1 citations
28 Sep 2022
TL;DR: In this paper , a method to find critical points of differentiable functionals in Banach spaces which belong to a suitable class (J ) of functionals is presented. But the problem of finding the critical points for a function in the Banach space is not addressed.
Abstract: . In this work, we establish a new method to find critical points of differentiable functionals defined in Banach spaces which belong to a suitable class ( J ) of functionals. Once given a functional J in the class ( J ), the central idea of the referred method consists in defining a real function ζ of a real variable, called energy function , which is naturally associated to J in the sense that the existence of real critical points for ζ guarantees the existence of critical points for the functional J . As a consequence, we are able to solve some variational elliptic problems, whose associated energy functional belongs to ( J ) and provide a version of the mountain pass theorem for functionals in the class ( J ) that allows us to obtain mountain pass solutions without the so-called Ambrosetti-Rabinowitz condition.
26 Oct 2022
TL;DR: In this paper , the existence of a solution for the following class of semipositone quasilinear problems was proved via nonsmooth critical points theory and comparison principle, and a solution exists for a small enough.
Abstract: This paper concerns the existence of a solution for the following class of semipositone quasilinear problems where 1 < p < N , a > 0, f : [0 , + ∞ ) → [0 , + ∞ ) is a function with subcritical growth and f (0) = 0, while h : R N → (0 , + ∞ ) is a continuous function that satisfies some technical conditions. We prove via nonsmooth critical points theory and comparison principle, that a solution exists for a small enough. We also provide a version of Hopf’s Lemma and a Liouville-type result for the p Laplacian in the whole R N . Mathematical Subject Classification MSC2010: 35J20, 35J62 (49J52).
TL;DR: In this paper , the existence of saddle-type solutions for a class quasilinear elliptic equations of the form [formula: see text] where [Formula:see text] is a N-function, and [FORMula:See text] was modeled on the Ginzburg-Landau potential was proved.
Abstract: In this work, we use variational methods to prove the existence of heteroclinic and saddle-type solutions for a class quasilinear elliptic equations of the form [Formula: see text] where [Formula: see text] is a N-function, [Formula: see text] is a periodic positive function and [Formula: see text] is modeled on the Ginzburg–Landau potential. In particular, our main result includes the case of the potential [Formula: see text], which reduces to the classical double well Ginzburg–Landau potential when [Formula: see text], that is, when we are working with the Laplacian operator.