Francisco Julio S. A. Corrêa

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.

Some non-local problems with nonlinear diffusion

Abstract In this paper we study different problems with nonlinear diffusion and non-local terms, some of them arising in population dynamics. We are able to give a complete description of the set of positive solutions and their stability. For that we employ a fixed point argument for the existence and uniqueness or multiplicity results and the study of singular eigenvalue problems for stability.

On the Existence of Solutions of a Nonlocal Elliptic Equation with a p-Kirchhoff-Type Term

Questions on the existence of positive solutions for the following class of elliptic problems are studied: , in , , on , where is a bounded smooth domain, and are given functions.

Existence of Solutions for Some Classes of Singular Hamiltonian Systems

Abstract This paper deals with existence of positive solution for the following singular Hamiltonian system where Ω ⊂ ℝN , N ≥ 2, is a smooth bounded domain and H, T, S, K are continuous functions. A key role is played by the Galerkin method.

A sub-supersolution approach for a quasilinear Kirchhoff equation

In this paper, we establish an existence result for a quasilinear Kirchhoff equation, via a sub- and supersolution approach, by using the Minty-Browder’s Theorem for pseudomonotone operators theory.

A variational approach to a nonlocal elliptic problem with sign-changing nonlinearity

Abstract In this paper we are concerned with the nonlocal elliptic problem where Ω ⊂ℝN is a bounded smooth domain, f, g : ℝ →ℝ are given functions and p is a fixed real number. We use variational methods to prove multiplicity results.

A VARIATIONAL APPROACH FOR A BI-NON-LOCAL ELLIPTIC PROBLEM INVOLVING THE p(x)-LAPLACIAN AND NON-LINEARITY WITH NON-STANDARD GROWTH

In this paper we are concerned with a class of p(x) -Kirchhoff equation where the non-linearity has non-standard growth and contains a bi-non-local term. We prove, by using variational methods (Mountain Pass Theorem and Ekeland Variational Principle), several results on the existence of positive solutions.

On a class of intermediate local-nonlocal elliptic problems

This paper is concerned with the existence of solutions for a class of intermediate local-nonlocal boundary value problems of the following type:

On the Existence of Infinite Sequences of Ordered Positive Solutions of Nonlinear Elliptic Eigenvalue Problems

-\rom{div} \bigg[a\bigg(\fint_{\Omega (x,r)}u(y)dy\bigg)\nabla u\bigg] = f(x,u,\nabla u ) \quad \mbox{in } \Omega, \ u\in H_{0}^{1}(\Omega ), \leqno{(\rom{IP})}