Infinitely many small energy solutions to the $ p $-Laplacian problems of Kirchhoff type with Hardy potential

Abstract

The present paper is devoted to obtaining the multiplicity result of solutions to the nonlinear elliptic equations of Kirchhoff type with Hardy potential. More precisely, the main purpose of this paper, under certain assumptions on the Kirchhoff function and nonlinear term, is to show the existence of infinitely many small energy solutions to the given problem. The primary tool is the dual fountain theorem to obtain the multiplicity result. Finally, by exploiting the dual fountain theorem and the modified functional method, we demonstrate that our problem has a sequence of infinitely many weak solutions, which converges to 0 in L ∞ -space.