### Necessary and sufficient condition for existence and uniqueness of nodal solutions to sublinear elliptic equations

Ryuji Kajikiya

#### Abstract

This paper deals with a sublinear elliptic equation $\Delta u + f(u)=0$ in a ball with the Dirichlet condition $u=0$ on the boundary. Under a suitable assumption on $f(\cdot)$, we establish the necessary and sufficient condition for the existence and uniqueness of radially symmetric nodal solutions.

#### Article information

Source
Adv. Differential Equations, Volume 6, Number 11 (2001), 1317-1346.

Dates
First available in Project Euclid: 2 January 2013