Existence of the Minimal Positive Solution of Some Nonlinear Elliptic Systems When the Nonlinearity is the Sum of a Sublinear and a Superlinear Term
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摘要: 证明了对每一λ∈(0,Λ),当Λ>0时半线性椭圆型方程组。有最小正解(λu,λv)。其中ΩRN(N≥2)为具有光滑边界的有界区域,0<q<1
u,λv关于λ是严格递增的。
Abstract: It is shown that there exists Λ>0 such that, for every λ∈(0,Λ), the semilinear elliptic system:-$u=λu|u|q-1+u|u|p-1-vinΩ, -$v=δu-γvin Ω,u=v=0 onΩ,where Ω∈RN>(N≥2) is a bounded domain with smooth boundary and 0<q<1<p,has a minimal positive solution (uλ,vλ). Moreover:uλ and vλ are strictly increasing with respect to λ.-
Key words:
- reaction diffusion system /
- positive solution /
- nonlinear equation
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