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

Abstract

This paper analyzes the nonlocal elliptic system involving the p(x)-biharmonic operator. We give the corresponding variational structure of the problem, and then by means of Ricceri’s Variational theorem and the definition of general Lebesgue-Sobolev space, we obtain sufficient conditions for the infinite solutions to this problem.

Infinitely many solutions for a nonlinear Navier problem involving the p-biharmonic operator

“…for each k ∈ N, and that the functional Φ + λΨ has no global minimum, it is necessary to use some sequences of functions defined ad hoc. Generally, in these functions the norm of the variable is raised to a suitable power which depends on the nature of the problem and that gives them the requested regularity properties: in some applications the norm is used without power (see, for instance, [3,7,14,15,23,27,39]), in some others it is raised to the second ( [9,10,29,33,35,36])…”

Multiple Solutions for a Nonlocal Elliptic Problem Involving p x

“…, p n )-Kirchhoff type problems. In [19], the author extended the conclusion of the problem (4) to the p(x)-biharmonic operator.…”