On a boundary value problem in the half-space

In this paper, we study the existence of positive solutions and sign-changing solutions for the following boundary value problem in the half-space { Δ u = 0 , in R + N + 1 , ∂ u ∂ n + λ g ( x ) u = f ( u ) , on ∂ R + N + 1 , where λ is a positive parameter and the nonlinear term f is superlinear at...

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Bibliographic Details
Published in:Journal of Differential Equations 2011-02, Vol.250 (4), p.2099-2142
Main Authors: Liu, Xiangqing, Liu, Jiaquan
Format: Article
Language:English
Subjects:
Asymptotically linear
Half-space
Sign-changing solution
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Summary:In this paper, we study the existence of positive solutions and sign-changing solutions for the following boundary value problem in the half-space { Δ u = 0 , in R + N + 1 , ∂ u ∂ n + λ g ( x ) u = f ( u ) , on ∂ R + N + 1 , where λ is a positive parameter and the nonlinear term f is superlinear at zero and asymptotically linear at infinity.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2010.11.001