二阶半正椭圆微分方程径向正解的存在性

Existence of radial positive solutions of second-order semi-positone elliptic differential equations

获得了二阶半正椭圆微分方程Δu+λg(|x|)f(u)=0,R_1<|x|<R_2,在Dirichlet和Robin边界条件下径向正解的存在性,其中g∈C([R_1,R_2],[0,+∞)),f∈C([0,+∞),R)。主要结果的证明基于锥上的不动点定理。

We consider the existence of radial positive solutions of second-order semi-positone elliptic differential equation Δu＋λg（｜x｜）f（u）=0,R_1〈｜x｜〈R2,with Dirichlet and Robin boundary conditions, where g∈C（[R1,R2],[0,＋∞））,f∈C（[0,＋∞）,R）.The proof of the main results are based on the fixed point theorems in cones.