摘要
本文用临界点方法讨论边值问题的经典解存在性问题,省去了关于f的有界性、非减性以及■存在性的假设条件获得某些较广的结果。
In the paper we consider the boundary value problems where f:R → R and g:[0,π]→ R are continuous mappings. Suppose that there is a mapping h: W_0^(1,2) (0,π)→ W_0^(1,2), h∈C^1(W_0^(1,2), W_0^(1,2), such that dh(u)(v)=f(u)v, W_0^(1,2)(0,π)is Sobolev space. First of all, we discuss the existence of critical points of the functional F, F: W_0^(1,2)(0,π)→R is defined by F(v) = integral from n=0 to π[v^2 + λv^2 + 2h(v)+ 2gv]dt, v∈W_0^(1,2)(0,π) Then, from the existence of critical points we obtain the main result as follows. Theorm 3 Suppose that Q(v)= =integral from n=0 to π[λv^2 +2h(v)]dt is a convex functional where dh(u)(v)=f(u)v, u,v∈W_0^(1,2)(0,π),h∈C^1(W_0^(1,2),W_0^(1,2)); Also that h(v)≥1/2μv^2 for any v∈W_0^(1,2)(0,π) almost everywhere on [0,π], where μ is a real number, then there exists a classical solution of the boundary value problems of Equation (1) if λ>-μ-2/π~2. The conditions about nondecreasing of the mapping f and the existence of (?) in some of Other papers are omitted here.
出处
《中国纺织大学学报》
CSCD
1989年第6期73-76,共4页
Journal of China Textile University
关键词
常微分方程
边值问题
凸函数
critical point, classical solution, weak solution, convex functional, boundary value problem
