Stationary quantum Zakharov systems involving a higher competing perturbation

Date

2020-01-10

Authors

Yao, Shuai
Sun, Juntao
Wu, Tsung-fang

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

We consider the stationary quantum Zakharov system with a higher competing perturbation Δ2u - Δu + λV(x)u = K(x)uφ - μ|u|p-2u in ℝ3, -Δφ + φ = K(x)u2 in ℝ3, where λ > 0, μ > 0, p > 4 and functions V and K are both nonnegative. Such problem can not be studied via the common arguments in variational methods, since Palais-Smale sequences may not be bounded. Using a constraint approach proposed by us recently, we prove the existence, multiplicity and concentration of nontrivial solutions for the above problem.

Description

Keywords

Quantum Zakharov system, Variational methods, Multiple solutions

Citation

Yao, S., Sun, J., & Wu, T. F. (2020). Stationary quantum Zakharov systems involving a higher competing perturbation. <i>Electronic Journal of Differential Equations, 2020</i>(06), pp. 1-18.

Rights

Attribution 4.0 International

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