Article ID Journal Published Year Pages File Type
841591 Nonlinear Analysis: Theory, Methods & Applications 2011 11 Pages PDF
Abstract

In this paper, we study the multiplicity of positive solutions for the following elliptic equation: {Δu−u=0in R+N,∂u∂ν=λa(x)|u|q−2u+b(x)|u|p−2uon ∂R+N, where 10} is an upper half space in RN,λ>0RN,λ>0 and the functions aa and bb are satisfying some suitable conditions. Using the decomposition of the Nehari manifold, we prove that the equation has at least two positive solutions provided λλ is sufficiently small.

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