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Kim, Chan-Gyun; Lee, Eun Kyoung

Existence of positive solutions to semilinear elliptic problems with nonlinear boundary condition. (English) Zbl 1404.35187

Proc. Indian Acad. Sci., Math. Sci. 128, No. 5, Paper No. 62, 8 p. (2018).
Summary: 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 the non-zero solution becomes a positive one for small \(\lambda>0\) under suitable assumptions on the perturbation term.

MSC:

35J61 Semilinear elliptic equations
35J66 Nonlinear boundary value problems for nonlinear elliptic equations
35B09 Positive solutions to PDEs

Keywords:

semilinear elliptic problem; nonlinear boundary condition; perturbed problem; positive solution
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References:

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