半线性椭圆方程径向正解的非存在性及解的振荡性和有界性的充分条件

Nonexistence of Radial Positive Solution, Sufficient Conditions of Oscillation and Boundedness of Radial Solution for Semilinear Elliptic Equation

设r=sum form i=1 to ∞(x_i^2),Ω={r|0≤r<a}是R^(?)中的开球。考虑无界域的二阶半线性椭圆方程边值问题: Δu+f(u,r)=0 r∈Ω′=R^n\(?) u|(?)Ω=0 r∈(?)Ω给出了问题径向正解的非存在性,解的振荡性及有界性的充分条件,并对有界解进行了估计。

In this paper we consider the following boundary value problem of the nonlinear second order elliptic partial differential equationwhere r is an open ball in R. The nonexistence theorem of radial positive solution, sufficient conditions of oscillation and boundedness of radial solution and estimation for bounded solution are given in this paper.