非线性高阶共振非局部边值问题  

Nonlinear higher-order nonlocal boundary value problems at resonance

作　　者：张海娥[1] 

机构地区：[1]唐山学院基础教学部,河北唐山063000

出　　处：《辽宁工程技术大学学报（自然科学版）》2014年第5期700-703,共4页Journal of Liaoning Technical University (Natural Science)

基　　金：国家自然科学基金资助项目(10801068);河北省高校科技研究基金资助项目(Z2013016);唐山市科技计划基金资助项目(12110233b)

摘　　要：针对一类新的非线性n阶共振非局部边值问题,运用Mawhin重合度理论,研究了边值问题解的若干存在性结论.结果表明:通过建立Sobolev空间和Banach空间,构造指标为零的Fredholm算子和满足适当条件的线性连续映射及其格林函数,当非线性项满足线性增长性条件时,同样可以得到共振边值问题解的存在性.该结果丰富了非线性高阶共振边值问题定解理论的相关成果,为工程实际问题提供了理论依据.For a new class of nth -order nonlocal boundary value problems at resonance, some existing resultswere concerned by using the coincidence degree theory of Mawhin, The results showed that the existence of solutions to boundary value problems at resonance was also obtained under linear growth assumptions on nonlinear terms by establishing Sobolev Space and Banach Space and constructing Fredholm operator of indexzero and a linear continuous projector satisfied suitable conditions and its Green function. The results enriched the relevant results of nonlinear boundary value problems at resonance and provided theoretical support of practical engineering problems.

关 键 词：非线性 高阶 非局部 共振 边值问题 存在性 格林函数 重合度理论 

分 类 号：O175[理学—数学]