Existence and multiplicity of solutions for a $p(x)$-Kirchhoff type problems

Abstract

This paper is concerned with the existence and multiplicity of solutions for a class of p(x)-Kirchhoff type equations with Neumann boundary condition. Our technical approach is based on variational methods.

Multiple Solutions for Nonlocal Elliptic Systems Involving p(x)-Biharmonic Operator

“…The nonlocal problems that arise in elasticity and population models and have attracted much attention in recent years, see [12][13][14][15][16][17][18][19]. In [14], Dai & Hao considered the nonlocal system…”

Infinitely many solutions for nonlocal problems with variable exponent and nonhomogeneous Neumann conditions

“…On the other hand, p(x)-Kirchhoff problems which are investigated on function spaces with variable exponents, have been studied by many researchers, see [15,16,20,21,23,24,34,35,37,56] and the references therein. For example, Dai and Hao in [20] by means of a direct variational approach and the theory of the variable exponent Sobolev spaces, established conditions ensuring the existence and multiplicity of solutions for the p(x)-Kirchhoff-type problem with Dirichlet boundary data.…”

Multiple solutions for Kirchhoff‐type problems with variable exponent and nonhomogeneous Neumann conditions

“…Recently, Kirchhoff type equations involving the ‐Laplacian have been investigated, but the results are rare. We refer the reader to for an overview of and references on this subject. For example, Chung in based on the mountain pass theorem combined with the Ekeland variational principle, obtained at least two distinct, non‐trivial weak solutions for a class of ‐Kirchhoff type equations with combined nonlinearities.…”