具有次线性和超线性项的非线性椭圆型方程组最小正解的存在性

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Existence of the Minimal Positive Solution of Some Nonlinear Elliptic Systems When the Nonlinearity is the Sum of a Sublinear and a Superlinear Term

Department of Mathematics, the Pennsylvania State University, University Park, PA 16902, U S A

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(λ_u,λ_v)。其中ΩR^N(N≥2)为具有光滑边界的有界区域,0<q<1u,λ_v关于λ是严格递增的。
- 反应扩散方程 /
- 正解 /
- 非线性方程
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∈R^N>(N≥2) is a bounded domain with smooth boundary and 0<q<1<p,has a minimal positive solution (u_λ,v_λ). Moreover:u_λ and v_λ are strictly increasing with respect to λ.
- reaction diffusion system /
- positive solution /
- nonlinear equation

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