Existence of solutions for an elliptic p(x)-Kirchhoff-type systems in unbounded domain

Abstract

In this paper we study of the existence of solutions for a class of elliptic system with nonlocal term in R N . The main tool used is the variational method, more precisely, the Mountain Pass Theorem.

On a class of fractional p(., .)-Kirchhoff-Schrödinger system type

“…Problems which involve the p(. )-Kirchhoff type have been intensively studied in the recent years, because of their numerous and relevant applications in many fields of mathematics, for example, electrorheological fluids (see [2]), elastic mechanics ( [1]), image restoration ( [7]). For this type of operator combined with a system of Kirchhoff functions we recall [1,5,11].…”

“…)-Kirchhoff type have been intensively studied in the recent years, because of their numerous and relevant applications in many fields of mathematics, for example, electrorheological fluids (see [2]), elastic mechanics ( [1]), image restoration ( [7]). For this type of operator combined with a system of Kirchhoff functions we recall [1,5,11]. Inspired by the above articles, we aim in this paper to prove, under minoration conditions on A i=1,2 and periodic conditions on F , the existence of solutions for the system (1) by applying variational method and Ekeland's principle.…”

Multiple Solutions for Ellipticpx,qx-Kirchhoff-Type Potential Systems in Unbounded

“…On the contrary, by using the mountain pass theorem, the authors in [24] showed the existence of nontrivial solutions for system (1)…”