Article ID Journal Published Year Pages File Type
4635555 Applied Mathematics and Computation 2007 11 Pages PDF
Abstract

In this paper, we study the nonlinear boundary value problem-Δu+u=fu(u,v)inΩ,-Δv+v=fv(u,v)inΩ,∂u∂n=gu(u,v),∂v∂n=gv(u,v)on∂Ω,where Ω   is a bounded domain in RNRN with smooth boundary and the pairs of (fu,fv)(fu,fv) and (gu,gv)(gu,gv) are subcritical nonlinearities. With the help of the Nehari manifold, we show existence of at least two positive solutions when one of the pairs of (fu,fv)(fu,fv) and (gu,gv)(gu,gv) is sublinear and the other one superlinear.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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