关于非线性两点边界值问题u"+g(t, u)=f(t), u(0)=u(2π)=0的解的存在性和唯一性

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On the Solution of Nonlinear Two-Point Boundary Value Problem u"+g(t, u)=f(t), u(0)=u(2π)=0

1.
Department of Mathematics and Physics Sciences, Wuxi University of Light Industry, Wuxi 214036, P.R. China;
2.
Department of Mathematics, Nanjing University, Nanjing 210008, P.R. China

摘要: 本文给出了max-min原理的一个非变分形式,证明了非线性两点边界值问题u"+g(t,u)=f(t),u(0)=u(2π)=0的解的一个存在性和唯一性定理.
- Hilbert空间 /
- 微分同胚 /
- 非线性两点边界值问题 /
- 唯一解
Abstract: In this paper,a non-variational version of a max-min principle is proposed,and an existence and uniqueness result is obtained for the nonlinear two-point boundary value problem u"+g(t,u)=f(t),u(0)=u(2π)=0.
- Hilbert space /
- diffeomorphism /
- nonlinear two-point boundary value problem /
- unique solution

[1]	R.F.Manasevich,A non variational version of a max-min principle,Nonlinear Analysis,Theory,Methods &Applications,7(6) (1983),565-570.
[2]	Gaetano Zampieri,Diffeomorphisms with Banach space domains,Nonlinear Analysis,Theory,Methods &Applications,19(10) (1992),923-932.