Existence and Multiplicity Solutions for the p$p$-Fractional Schrödinger–Kirchhoff Equations with Electromagnetic Fields and Critical Nonlinearity

Abstract

This paper is devoted to the study of the $p$-fractional Schrodinger–Kirchhoff equations with electromagnetic fields and critical nonlinearity. By using the variational methods, we obtain the existence of mountain pass solutions $u_{\varepsilon }$ which tend to the trivial solutions as $\varepsilon \rightarrow 0$. Moreover, we get $m^{\ast }$ pairs of solutions for the problem in absence of magnetic effects under some extra assumptions.