Fourth order Hamiltonian system with some singular nonlinear term and multiplicity result

Boundary value problems

Q-Heung Choi¹  Tacksun Jung² 

[1] Department of Mathematics Education, Inha University, Incheon, Korea;Department of Mathematics, Kunsan National University, Kunsan, Korea

关键词: fourth order Hamiltonian system;    singular nonlinear term;    variational method;    critical point theory;    minimax method;    homology theory;    \((P.S.)_{c}\) condition;    35Q72;   

DOI  :  10.1186/s13661-016-0638-z

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We consider a fourth order Hamiltonian system with some singular nonlinear term and multiplicity result. We get two theorems which show the number of weak solutions of this problem. The first theorem is a result which shows that there exists a weak solution for this problem and the second one is an improved result of the first result, which shows that there exist infinitely many weak solutions for this problem. We get the first result by a variational method and critical point theory, and we get the second result by homology theory.

【 授权许可】

CC BY