带有非线性边界条件的椭圆方程的解的存在性

广东工业大学学报 ›› 2011, Vol. 28 ›› Issue (4): 30-33.

带有非线性边界条件的椭圆方程的解的存在性

广东工业大学应用数学学院，广东广州 510006

出版日期:2011-12-25 发布日期:2011-12-25
作者简介:朱红波(1980-)，女，讲师，博士，主要研究方向为非线性偏微分方程.
基金资助:
国家自然科学基金资助项目(11026138)

Solutions to an Asymptotically Linear Elliptic Problem with Nonlinear Boundary Conditions

Faculty of Applied Mathematics, Guangdong University of Technology, Guangzhou 510006, China

Online:2011-12-25 Published:2011-12-25

摘要/Abstract

摘要： 研究空间Ω上带有非线性边界条件的椭圆型方程的非平凡解，其中Ω是RN(N≥3)中的有界光滑区域，非线性项f(x,s)关于s在无穷远处渐近线性. 应用Ekeland’s变分原理和Mountain Pass定理,证明当非负参数〖QX(Y12〗SymbollAp〖QX)〗充分小时，方程至少存在两个不同的非平凡解.

关键词: 渐近线性；非线性边界条件；Mountain Pass定理

Abstract: It studies the existence of nontrivial solutions to an asymptotically linear elliptic problem with nonlinear boundary conditions on Ω，where Ω is a bounded smooth domain in RN(N≥3), and the nonlinear term f(x,u) is asymptotically linear with respect to u at infinity. By Ekeland’s variational principle and a variant version of Mountain Pass Theorem, it proves that there exist at least two nontrivial solutions if the nonnegative parameter SymbollA is small enough.

Key words: asymptotically linear; nonlinear boundary conditions; Mountain Pass Theorem

朱红波. 带有非线性边界条件的椭圆方程的解的存在性[J]. 广东工业大学学报, 2011, 28(4): 30-33.

ZHU Hong-Bo-. Solutions to an Asymptotically Linear Elliptic Problem with Nonlinear Boundary Conditions[J]. Journal of Guangdong University of Technology, 2011, 28(4): 30-33.

参考文献

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