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

Rabil Ayazoglu, Yesim Sarac, S. Şule Şener, Gülizar Alisoy

• 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.