Existence results for nonlinear Schrodinger equations involving the fractional (p,q)-Laplacian and critical nonlinearities
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Date
2021-12-20
Authors
Lv, Huilin
Zheng, Shenzhou
Feng, Zhaosheng
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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 ℝn,
(-∆)s1pu + (-∆)s2qu + V(εx) (|u|p-2 u + |u|q-2 u) = λƒ(u) + σ|u|q*s2-2 u.
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.
Description
Keywords
Nonlinear Schrödinger equations, Nonlocal (p,q)-Laplacian, Critical growth, Rabinowitz potentials, Nehari manifold
Citation
Lv, H., Zheng, S., & Feng, Z. (2021). Existence results for nonlinear Schrodinger equations involving the fractional (p,q)-Laplacian and critical nonlinearities. <i>Electronic Journal of Differential Equations, 2021</i>(100), pp. 1-24.