EXISTENCE OF THE MINIMAL POSITIVE SOLUTION OF SOME NONLINEAR ELLIPTIC SYSTEMS WHEN THE NONLINEARITY IS THE SUM OF A SUBLINEAR AND A SUPERLINEAR TERM  

作　　者：Nicolae Tarfulea (Department of Mathematics, the Pennsylvania State University, University Park, PA 16802, U S A) 

出　　处：《Applied Mathematics and Mechanics(English Edition)》2000年第3期283-290,共8页应用数学和力学（英文版）

摘　　要：It is shown that there exists Λ>0 such that, for every λ∈(0,Λ), the semilinear elliptic system: - Δ u=λu｜u｜ q-1 +u｜u｜ p-1 -v inΩ, - Δ v=δu-γv in Ω, u=v=0 on Ω, 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.It is shown that there exists Λ>0 such that, for every λ∈(0,Λ), the semilinear elliptic system: - Δ u=λu｜u｜ q-1 +u｜u｜ p-1 -v inΩ, - Δ v=δu-γv in Ω, u=v=0 on Ω, 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.

关 键 词：reaction diffusion system positive solution nonlinear equation 

分 类 号：O175.25[理学—数学]