### 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

Mathematical Reviews number (MathSciNet)
MR1859350

Zentralblatt MATH identifier
1010.35040

#### Citation

Kajikiya, Ryuji. Necessary and sufficient condition for existence and uniqueness of nodal solutions to sublinear elliptic equations. Adv. Differential Equations 6 (2001), no. 11, 1317--1346. https://projecteuclid.org/euclid.ade/1357139963.