arXiv subjects
Publications and source records attributed to Jefferson A. Santos.
In this work we estend a recent result of Kristály, Marzantowicz and Varga concerning the existence of three critical points certain non-smooth functionals. Using this result, we guarantee the existence of three solutions to a inclusion quasilinear problem, with non-homogeneous boundary condition through Orlicz Sobolev spaces.
In this work we study the existence of nontrivial solution for the following class of multivalued elliptic problems $$ -Δu+V(x)u-εh(x)\in \partial_t F(x,u) \quad \text{in} \quad \mathbb{R}^2, \eqno{(P)} $$ where $ε>0$, $V$ is a continuous function verifying some conditions, $h \in (H^{1}(\mathbb{R}^{2}))^{*}$ and $\partial_t F(x,u)$ is a generalized gradient of $F(x,t)$ with respect to $t$ and $F(x,t)=\int_{0}^{t}f(x,s)\,ds$. Assuming that $f$ has an exponential critical growth and a discontinuity point, we have applied Variational Methods for locally Lipschitz functional to get two solutions for $(P)$ when $ε$ is small enough.
We show the existence of a nodal solution with two nodal domains for a generalized Kirchhoff equation of the type $$ -M\left(\displaystyle\int_ΩΦ(|\nabla u|)dx\right)Δ_Φu = f(u) \ \ \mbox{in} \ \ Ω, \ \ u=0 \ \ \mbox{on} \ \ \partialΩ, $$ where $Ω$ is a bounded domain in $\mathbf{R}^N$, $M$ is a general $C^{1}$ class function, $f$ is a superlinear $C^{1}$ class function with subcritical growth, $Φ$ is defined for $t\in \mathbf{R}$ by setting $ Φ(t)=\int_0^{|t|}ϕ(s)sds$, $Δ_Φ$ is the operator $Δ_Φu:=div(ϕ(|\nabla u|)\nabla u)$. The proof is based on a minimization argument and a quantitative deformation lemma.
In this work, we study the existence and multiplicity of solutions for a class of problems involving the $ϕ$-Laplacian operator in a bounded domain, where the nonlinearity has a critical growth. The main tool used is the variational method combined with the genus theory for even functionals.
This paper is concerned with the multiplicity of nontrivial solutions in an Orlicz-Sobolev space for a nonlocal problem involving N-functions and theory of locally Lispchitz continuous functionals.
This paper is concerned with the multiplicity of nontrivial solutions in an Orlicz-Sobolev space for a nonlocal problem with critical growth, involving N-functions and theory of locally Lispchitz continuous functionals.
The main goal this work is to prove two results like Strauss and Lions for Orlicz-Sobolev spaces. After, we use these results for study the existence of solutions for a class of quasilinear problems in $\mathbb{R}^{N}$.