Solutions to an Asymptotically Linear Elliptic Problem with Nonlinear Boundary Conditions

ZHU  Hong-Bo

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Solutions to an Asymptotically Linear Elliptic Problem with Nonlinear Boundary Conditions

更新时间：2026-05-27

- Solutions to an Asymptotically Linear Elliptic Problem with Nonlinear Boundary Conditions
- Vol. 28, Issue 4, Pages: 30-33(2011)
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- Online First：25 December 2011，
  
  Published：2011
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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]. 2011, 28(4): 30-33.
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. DOI：

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

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λ充分小时，方程至少存在两个不同的非平凡解.

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 λ is small enough.

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references

Adams R A, Journier J. Sobolev Spaces[M]. Second edition.Amsterdam:Acad Press,2003.

Garcia Azorero J, Peral I, Rossi J D. A convex-concave problem with a nonlinear boundary condition[J]. J Differential Equations， 2004(198): 91-128.

Terraccini S. Symmetry properties of positive solutions to some elliptic equations with nonlinear boundary conditions[J]. Differential Integral Equations, 1995(8):1911-1922.

Ambrosetti A, Rabinowitz P. Dual variational methods in critical points theory and applications[J]. J Funct Anal,1973(14):349-381.

Ekeland I. Nonvex minimization problems[J]. Bull Amer Math Soc, 1979(1): 443-473.

Li Shujie, Wu Shaoping, Zhou Huansong. Solutions to semilinear elliptic problems with combined nonlinearities[J]. J Differential Equations, 2002(185):200-224.

Schechter M. A variation of the Mountain Pass lemma and applications[J]. J London Math Soc, 1991(44): 491-502.

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Related Author

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Related Institution

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