Multiple solutions for a fourth-order elliptic equation of Kirchhoff type with variable exponent

Abstract

In this paper, we consider a class of fourth-order elliptic equations of Kirchhoff type with variable exponent [Formula: see text] where [Formula: see text], [Formula: see text], is a smooth bounded domain, [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] is the operator of fourth-order called the [Formula: see text]-biharmonic operator, [Formula: see text] is the [Formula: see text]-Laplacian, [Formula: see text] is a log-Hölder continuous function and [Formula: see text] is a continuous function satisfying some certain conditions. A multiplicity result for the problem is obtained by using the mountain pass theorem and Ekeland’s variational principle provided [Formula: see text] is small enough.