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 Rn,
We prove existence by confining different ranges of the parameter λ under the subcritical or critical nonlinearities caused by σ=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.
Lv, Huilin, Shenzhou Zheng, and Zhaosheng Feng. "Existence results for nonlinear Schrodinger equations involving the fractional (p, q)-Laplacian and critical nonlinearities." Electronic Journal of Differential Equations 2021.100 (2021): 1-24.
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Electron. J. Differential Equations