Multiple Solutions to a Non-Local Problem of Schrödinger–Kirchhoff Type in ℝ^<i>N</i>

Abstract

The main purpose of this paper is to show the existence of a sequence of infinitely many small energy solutions to the nonlinear elliptic equations of Kirchhoff–Schrödinger type involving the fractional p-Laplacian by employing the dual fountain theorem as a key tool. Because of the presence of a non-local Kirchhoff coefficient, under conditions on the nonlinear term given in the present paper, we cannot obtain the same results concerning the existence of solutions in similar ways as in the previous related works. For this reason, we consider a class of Kirchhoff coefficients that are different from before to provide our multiplicity result. In addition, the behavior of nonlinear terms near zero is slightly different from previous studies.

Keywords

• fractional <i>p</i>-Laplacian
• Kirchhoff function
• weak solution
• dual fountain theorem