一类相对非线性薛定谔方程解的存在性

Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (1): 95-104.

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Existence of Nontrivial Solutions for a Class of Relativistic Nonlinear Schrödinger Equations

Wen Qiu^1,²,Yimin Zhang^1,^2,*(),Ahmed Adam Abdelgadir³

¹ Center of Mathematical Sciences, Wuhan University of Technology, Wuhan 430070
² Department of Mathematics, School of Science, Wuhan University of Technology, Wuhan 430070
³ Department of Mathematics, Taibah University Madinah Munawwarah, Saudi Arabia

Received:2017-12-27 Online:2019-02-26 Published:2019-03-12
Contact: Yimin Zhang E-mail:loiolo@qq.com; zhangym802@126.com; ahmedguangzhou17@gmail.com
Supported by:
the NSFC(11471330);the NSFC(11501555);the NSFC(11771127);the Fundamental Research Funds for the Central Universities(2017IVA-075);the Fundamental Research Funds for the Central Universities(2017IVA076);the Fundamental Research Funds for the Central Universities(2018-zy-138);the Fundamental Research Funds for the Central Universities(2018IB014)

Abstract

Abstract:

Using the critical point theory, we consider a class of relativistic nonlinear Schrödinger equations. By introducing a change, we transform the relativistic nonlinear Schrödinger equations into the semilinear elliptic equations. First, we extend results of the classical field equation to the relativistic nonlinear Schrödinger equation. Then, the variational methods was used to obtain the existence of nontrivial solutions of the relativistic nonlinear Schrödinger equations with bounded potential. Moreover, we improved the general superlinear conditions which was used in [12-13].

Key words: Mountain pass theorem, Relativistic nonlinear Schrödinger equation, Concentration compactness principle

CLC Number:

O175.25

Wen Qiu,Yimin Zhang,Ahmed Adam Abdelgadir. Existence of Nontrivial Solutions for a Class of Relativistic Nonlinear Schrödinger Equations[J].Acta mathematica scientia,Series A, 2019, 39(1): 95-104.

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References 16

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Existence of Nontrivial Solutions for a Class of Relativistic Nonlinear Schrödinger Equations

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