摘要
证明了对每一 λ∈ (0 ,Λ) ,当Λ >0时半线性椭圆型方程组 -Δu=λu｜u｜q- 1+u｜u｜p- 1-v (在Ω中 ) ,-Δv =δu-γv (在Ω中 ) ,u=v=0 (在 Ω上 ) · 有最小正解(uλ,vλ) · 其中Ω RN(N≥ 2 )为具有光滑边界的有界区域 ,0 <q <1<p· 并且uλ,vλ 关于λ是严格递增的·
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 in Ω, - 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.
出处
《应用数学和力学》
CSCD
北大核心
2000年第3期253-259,共7页
Applied Mathematics and Mechanics
