Giovany M. Figueiredo

On an elliptic equation of p -Kirchhoff type via variational methods

This paper is concerned with the existence of positive solutions to the class of nonlocal boundary value problems of the p -Kirchhoff type and where Ω is a bounded smooth domain of ℝ N , 1 p N , s ≥ p * = ( p N )/( N – p ) and M and f are continuous functions.

On a p-Kirchhoff equation via Krasnoselskii’s genus

Abstract In this work will use the genus theory, introduced by Krasnoselskii, to show a result of existence and multiplicity of solutions of the p -Kirchhoff equation − [ M ( ∫ Ω | ∇ u | p d x ) ] p − 1 Δ p u = f ( x , u ) in Ω , u = 0 on ∂ Ω where Ω is a bounded smooth domain of R N , 1 p N , and M and f are continuous functions.

Multiplicity of Positive Solutions For a Quasilinear Problem in IRN Via Penalization Method

Abstract The multiplicity and concentration of positive solutions are established for the equation −εpΔpu + V (z)|u|p-2u = f(u) in IRN, where V is a positive continuous function and f ∈ C1 is a function having subcritical and superlinear growth.

On a fractional Kirchhoff-type equation via Krasnoselskii’s genus

In this paper we study a highly nonlocal problem involving a fractional operator combined with a Kirchhoff-type coefficient. The latter is allowed to vanish at the origin (degenerate case). Precisely, we consider the following nonlocal problem ⎧

On the existence of positive solution for an elliptic equation of Kirchhoff type via Moser iteration method

We investigate the questions of existence of positive solution for the nonlocal problem and on, where is a bounded smooth domain of, and and are continuous functions.

Strauss and Lions type results for a class of Orlicz-Sobolev spaces and applications

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

Existence of solutions for a nonlinear Choquard equation with potential vanishing at infinity

\mathbb{R}^{N}

Quasilinear equations with dependence on the gradient via Mountain Pass techniques in RN

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Multiplicity and Concentration of Positive Solutions for a Class of Quasilinear Problems

Abstract We study the following nonlinear Choquard equation: - Δ ⁢ u + V ⁢ ( x ) ⁢ u = ( 1 | x | μ ∗ F ⁢ ( u ) ) ⁢ f ⁢ ( u )   in ⁢ ℝ N ,

Existence of a least energy nodal solution for a Schrödinger-Kirchhoff equation with potential vanishing at infinity

-\Delta u+V(x)u=\biggl{(}\frac{1}{|x|^{\mu}}\ast F(u)\biggr{)}f(u)\quad\text{% in }\mathbb{R}^{N},