Existence results for nonlinear Schrodinger equations involving the fractional (p,q)-Laplacian and critical nonlinearities

Abstract

In this article, we consider the existence of ground state positive solutions for nonlinear Schrodinger equations of the fractional (p,q)-Laplacian with Rabinowitz potentials defined in \(R^n\), $$ ( -\Delta ) _p^{s_1}u+( -\Delta )_q^{s_2}u+V( \epsilon x) ( | u|^{p-2}u+| u| ^{q-2}u) =\lambda f( u) +\sigma | u| ^{q_{s_2}^{\ast }-2}u. $$ We prove existence by confining different ranges of the parameter \(\lambda\) under the subcritical or critical nonlinearities caused by \(\sigma=0\) or 1, respectively. In particular, a delicate calculation for the critical growth is provided so as to avoid the failure of a global Palais-Smale condition for the energy functional.
 For more information see https://ejde.math.txstate.edu/Volumes/2021/100/abstr.html