Existence of positive solutions to semilinear elliptic problems with nonlinear boundary condition

Proceedings of the Indian Academy of Sciences. Mathematical sciences

CHAN-GYUN KIM^1¹ 

[1] Department of Mathematics Education, Pusan National University, Busan 609-735, Korea^1

关键词: Semilinear elliptic problem;    nonlinear boundary condition;    perturbed problem;    positive solution;    multiplicity;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

In this paper, a semilinear elliptic equation with a nonlinear boundary condition and a perturbation in the reaction term is studied. The existence of a positive solution and another non-zero solution to the problem is proved when $|\lambda|$ is small enough without any specific assumptions on the perturbation term. Moreover, it is shown that thenon-zero solution becomes a positive one for small $\lambda$ > 0 under suitable assumptions on the perturbation term.

【 授权许可】

CC BY