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

作　　者：罗华 LUO Hua(Department of Mathematics,Dongbei University of Finance and Economics,Dalian 116025,China)

机构地区：[1]东北财经大学数学学院,辽宁大连116025

出　　处：《高校应用数学学报（A辑）》2018年第3期303-314,共12页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11301059;71571035);辽宁省优秀人才支持计划(LJQ2014128)

摘　　要：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.

关 键 词：V时标 加权共振问题 可解性 多解性 Lyapunov-Schmidt过程 

分 类 号：O175.8[理学—数学]