Multiple solutions of p-fractional Schrödinger-Choquard-Kirchhoff equations with Hardy-Littlewood-Sobolev critical exponents

Abstract

In this article, we are concerned with multiple solutions of Schrödinger-Choquard-Kirchhoff equations involving the fractional pp-Laplacian and Hardy-Littlewood-Sobolev critical exponents in RN{{\mathbb{R}}}^{N}. We classify the multiplicity of the solutions in accordance with the Kirchhoff term M(⋅)M\left(\cdot ) and different ranges of qq shown in the nonlinearity f(x,⋅)f\left(x,\cdot ) by means of the variational methods and Krasnoselskii’s genus theory. As an immediate consequence, some recent related results have been improved and extended.

Keywords

• fractional p-laplacian
• multiple solutions
• hardy-littlewood-sobolev’s critical exponents
• concentration-compactness
• genus theory
• 35a15
• 35j60
• 35j20