Multiple solutions of <i>p</i>-fractional Schrödinger-Choquard-Kirchhoff equations with Hardy-Littlewood-Sobolev critical exponents
Xiaolu Lin, Shenzhou Zheng, Zhaosheng Feng
Abstract
Abstract In this article, we are concerned with multiple solutions of Schrödinger-Choquard-Kirchhoff equations involving the fractional <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>p</m:mi> </m:math> p -Laplacian and Hardy-Littlewood-Sobolev critical exponents in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mrow> <m:mi mathvariant="double-struck">R</m:mi> </m:mrow> <m:mrow> <m:mi>N</m:mi> </m:mrow> </m:msup> </m:math> {{\mathbb{R}}}^{N} . We classify the multiplicity of the solutions in accordance with the Kirchhoff term <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>M</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mo>⋅</m:mo> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> M\left(\cdot ) and different ranges of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>q</m:mi> </m:math> q shown in the nonlinearity <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>f</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>x</m:mi> <m:mo>,</m:mo> <m:mo>⋅</m:mo> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> 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.