Multiple positive solutions for semilinear elliptic systems with nonlinear boundary condition

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.