Existence and multiplicity of solutions for a Schrödinger–Kirchhoff type equation involving the fractional p(. ,.) -Laplacian operator in RN

In this paper, by using variational approach, Mountain Pass Theorem and Krasnoselskii’s genus theory, we show the existence and multiplicity of solutions for a Schrödinger–Kirchhoff type equation involving the fractional p(. ,.) -Laplacian in fractional Sobolev space with variable exponent. We also establish a Bartsch–Wang type compact embedding theorem for fractional Sobolev space with variable exponent.