Electron. J. Differential Equations, Vol. 2020 (2020), No. 06, pp. 1-18.

Stationary quantum Zakharov systems involving a higher competing perturbation

Shuai Yao, Juntao Sun, Tsung-Fang Wu

Abstract:
We consider the stationary quantum Zakharov system with a higher competing perturbation

where $\lambda >0$, $\mu>0$, $p>4$ 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.

Submitted July 21, 2019. Published January 10, 2020.
Math Subject Classifications: 35J35, 35B38.
Key Words: Quantum Zakharov system; variational methods; multiple solutions.
DOI: 10.58997/ejde.2020.06

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Shuai Yao
School of Mathematics and Statistics
Shandong University of Technology
Zibo 255049, China
email: shyao2019@163.com
Juntao Sun
School of Mathematics and Statistics
Shandong University of Technology
Zibo 255049, China
email: jtsun@sdut.edu.cn
Tsung-Fang Wu
Department of Applied Mathematics
National University of Kaohsiung
Kaohsiung 811, Taiwan
email: tfwu@nuk.edu.tw

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