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

Authors

Huilin Lv
Shenzhou Zheng
Zhaosheng Feng, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

12-20-2021

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)(s1) u + (-Delta)(q)(s2) q u+ V(epsilon x)(vertical bar u vertical bar(p-2)u+vertical bar u vertical bar(q-2)u) =lambda f(u) + sigma vertical bar u vertical bar q*(-2)(s2)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.

Comments

© 2021.

Recommended Citation

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.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Publication Title

Electron. J. Differential Equations