School of Mathematical and Statistical Sciences Faculty Publications and Presentations
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.
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
Comments
© 2021.