Existence of multiple nontrivial solutions of the nonlinear Schrödinger-Korteweg-de Vries type system

Advances in Nonlinear Analysis

Yang Jing¹  Geng Qiuping²  Wang Jun² 

[1] College of Science, Jiangsu University of Science and Technology, Zhenjiang, 212003, P. R. China;Institute of Applied System Analysis, Jiangsu University, Zhenjiang, Jiangsu, 212013, P.R. China;

关键词: positive solutions;    bifurcation theory;    critical points;    nonlinear schrödinger-korteweg-de vries system;    35j61;    35j20;    35q55;    49j40;   

DOI  :  10.1515/anona-2021-0214

来源: DOAJ

【 摘 要 】

In this paper we are concerned with the existence, nonexistence and bifurcation of nontrivial solution of the nonlinear Schrödinger-Korteweg-de Vries type system(NLS-NLS-KdV). First, we find some conditions to guarantee the existence and nonexistence of positive solution of the system. Second, we study the asymptotic behavior of the positive ground state solution. Finally, we use the classical Crandall-Rabinowitz local bifurcation theory to get the nontrivial positive solution. To get these results we encounter some new challenges. By combining the Nehari manifolds constraint method and the delicate energy estimates, we overcome the difficulties and find the two bifurcation branches from one semitrivial solution. This is an new interesting phenomenon but which have not previously been found.

【 授权许可】

Unknown