Banach空间二阶边值问题解的存在性  

Existence of solutions for second order boundary value problems in Banach spaces

作　　者：杨艳[1] 

机构地区：[1]西北师范大学数学与信息科学学院,甘肃兰州730070

出　　处：《西北师范大学学报（自然科学版）》2010年第5期10-12,共3页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(10871160);甘肃省自然科学基金资助项目(0710RJZA103)

摘　　要：讨论了Banach空间中非线性二阶Dirichlet边值问题解的存在性.在非线性项满足较弱的非紧性测度条件及线性增长条件下,应用凝聚映射的拓扑度理论获得了该问题解的存在性.这个线性增长条件是保证解存在的最优条件.This paper discusses the existence of solutions for nonlinear second order Dirichlet boundary value problem in Banach spaces.Under a weaker condition of noncompactness measure and a linear growth condition on the nonlinearity,an existence result is obtained by employing the topological degree theory of condensing mapping.The linear growth condition is optimal to guarantee the existence of solutions.

关 键 词：二阶边值问题 存在性 凝聚映射 拓扑度 

分 类 号：O175.15[理学—数学]