## The radial solution of 2-order semilinear elliptic equation.(Chinese. English summary)Zbl 0864.35040

Summary: This paper discusses the boundary value problem for the semilinear elliptic equation $$\Delta u=f(u)$$ in $$\mathbb{R}^N$$ with $$f\in C(\mathbb{R})$$, $$uf(u)>0$$, $$f(0)=0$$; it gives properties of the classical radial solution, and proves existence and nonexistence and uniqueness. Further, estimations of the radial solution are also given.

### MSC:

 35J65 Nonlinear boundary value problems for linear elliptic equations

### Keywords:

existence; nonexistence; uniqueness