非线性加权V时标动态方程共振问题的可解性与多解性

Existence and multiplicity of solutions for a weight nonlinear V-time scales boundary value problems at resonance

基于对应线性问题的谱结构,对一类非线性加权V时标动态方程共振问题,在允许非线性项无界,但是次线性增长的前提下,获得了符号条件下一个解和多个解的存在性,所用的研究方法是含参紧向量场的解集连通理论.

This paper obtains the existence and multiplicity of solutions for a nonlinear V-time scales boundary value problem at resonance.The existence results allow that nonlinear term is an unbounded function with the sublinear growth condition and a sign condition.The discussion is based upon spectrum structure of the corresponding linear problem.The main tool is the connectivity properties of solution sets of parameterized families of compact vector fields.