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

Date

2021-12-20

Authors

Lv, Huilin
Zheng, Shenzhou
Feng, Zhaosheng

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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.

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Attribution 4.0 International

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