Article ID Journal Published Year Pages File Type
841648 Nonlinear Analysis: Theory, Methods & Applications 2010 8 Pages PDF
Abstract

We prove the existence of nonnegative solutions to the system −Δu=λa(x)f(v)in Ω,−Δv=λb(x)g(u)in Ω,u=0=von ∂Ω, where ΩΩ is a bounded domain in RNRN with a smooth boundary ∂Ω,λ∂Ω,λ is a positive parameter. By the method of monotone iteration and Schauder fixed point theorem, we prove the existence of a nonnegative solution to the above system for λλ sufficiently small. In this study, we do not restrict the sign of aa and bb.

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