一类半线性椭圆型方程组正解的局部存在唯一性

The Local Existence and Uniqueness of Positive Solution for Semilinear Elliptic Systems

考虑带有参数λ的半线性椭圆型方程组{λΔu+vp=0,x∈RnλΔv+wp=0,x∈RnλΔw+up=0,x∈Rnlim|x|→∞u=lim|x|→∞v=lim|x|→∞w=0,x∈Rn正解的局部存在唯一性,其中u,v,w∈C2(Rn),p≥1,λ≠0.

The local existence and uniqueness of positive solution for a class of Lane-Emden type semilinear elliptic systems of three equations with a parameter are studied, Where {λΔu＋vp=0,x∈RnλΔv＋wp=0,x∈RnλΔw＋up=0,x∈Rnlim｜x｜→∞u=lim｜x｜→∞v=lim｜x｜→∞w=0,x∈RWhere u,v,w∈C2（Rn）,p≥1,λ≠0.