Multiplicity of solutions to non-local problems of Kirchhoff type involving Hardy potential

Abstract

The aim of this paper is to establish the existence of a sequence of infinitely many small energy solutions to nonlocal problems of Kirchhoff type involving Hardy potential. To this end, we used the Dual Fountain Theorem as a key tool. In particular, we describe this multiplicity result on a class of the Kirchhoff coefficient and the nonlinear term which differ from previous related works. To the best of our belief, the present paper is the first attempt to obtain the multiplicity result for nonlocal problems of Kirchhoff type involving Hardy potential by utilizing the Dual Fountain Theorem.

Keywords

• fractional $ p $-laplacian
• kirchhoff function
• hardy potential
• weak solution
• dual fountain theorem