Stationary quantum Zakharov systems involving a higher competing perturbation
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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. Electronic Journal of Differential Equations, 2020(06), pp. 1-18.
Rights
Attribution 4.0 International