Existence of solutions for subquadratic convex operator equations at resonance and applications to Hamiltonian systems

Advances in Difference Equations

article

Song, Mingliang¹  Chen, Ping² 

[1] School of Mathematical Sciences, Nanjing Normal University;Mathematics and Information Technology School, Jiangsu Second Normal University

关键词: Operator equations;    Subquadratic;    Index theory;    Dual least action principle;    Convex Hamiltonian systems;   

DOI  :  10.1186/s13662-020-02947-9

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

This paper investigates the existence of solutions to subquadratic operator equations with convex nonlinearities and resonance by means of the index theory for self-adjoint linear operators developed by Dong and dual least action principle developed by Clarke and Ekeland. Applying the results to subquadratic convex Hamiltonian systems satisfying several boundary value conditions including Bolza boundary value conditions, generalized periodic boundary value conditions and Sturm–Liouville boundary value conditions yield some new theorems concerning the existence of solutions or nontrivial solutions. In particular, some famous results about solutions to subquadratic convex Hamiltonian systems by Mawhin and Willem and Ekeland are special cases of the theorems.

【 授权许可】

CC BY