On a class of nonlocal elliptic systems of ðp; qÞ-Kirchhoff type

Document Type : Original Article

Authors

1 University Mohamed I, Faculty of Sciences, Department of Mathematics, Oujda, Morocco

2 CRMEF, Oujda, Morocco

Abstract

In this paper, we establish the existence of at least three solutions for the following nonlocal elliptic system of ðp; qÞ-Kirchhoff type  M1
R
X jruj
p
dx     p1
Dpu ¼ kFuðx; u; vÞ þ lGuðx; u; vÞ
in X;  M2
R
X jrvj
q
dx     q1
Dqv ¼ kFvðx; u; vÞ þ lGvðx; u; vÞ in X; u ¼ v ¼ 0 on @X. Our technical
approach is based on the three critical points theorem of Ricceri.

Keywords