Differential and Integral Equations

Nodal solutions to semilinear elliptic equations in a ball

Walter Dambrosio

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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

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

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34B15: Nonlinear boundary value problems
Secondary: 35J25: Boundary value problems for second-order elliptic equations 35J60: Nonlinear elliptic equations


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

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