## Differential and Integral Equations

- Differential Integral Equations
- Volume 15, Number 8 (2002), 945-972.

### Nodal solutions to semilinear elliptic equations in a ball

#### Abstract

In this paper we are concerned with the existence and multiplicity of nodal solutions to the Dirichlet problem associated to the elliptic equation $\Delta u+q(|x|)g(u)=0$ in the unit ball in ${\bf R}^N$. The nonlinearity $g$ has a linear growth at infinity and zero, while the weight function $q$ is nonnegative in $[0,1]$ and strictly positive in some interval $[r_1,r_2]\subset [0,1]$. By means of a topological degree approach, we are able to prove the existence of solutions with prescribed nodal properties, depending on the behaviour of the ratio $g(u)/u$ at infinity and zero.

#### Article information

**Source**

Differential Integral Equations, Volume 15, Number 8 (2002), 945-972.

**Dates**

First available in Project Euclid: 21 December 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1356060780

**Mathematical Reviews number (MathSciNet)**

MR1895574

**Zentralblatt MATH identifier**

1024.34009

**Subjects**

Primary: 34B15: Nonlinear boundary value problems

Secondary: 35J25: Boundary value problems for second-order elliptic equations 35J60: Nonlinear elliptic equations

#### Citation

Dambrosio, Walter. Nodal solutions to semilinear elliptic equations in a ball. Differential Integral Equations 15 (2002), no. 8, 945--972. https://projecteuclid.org/euclid.die/1356060780