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2002 Nodal solutions to semilinear elliptic equations in a ball
Walter Dambrosio
Differential Integral Equations 15(8): 945-972 (2002).

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.

Citation

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Walter Dambrosio. "Nodal solutions to semilinear elliptic equations in a ball." Differential Integral Equations 15 (8) 945 - 972, 2002.

Information

Published: 2002
First available in Project Euclid: 21 December 2012

zbMATH: 1024.34009
MathSciNet: MR1895574

Subjects:
Primary: 34B15
Secondary: 35J25, 35J60

Rights: Copyright © 2002 Khayyam Publishing, Inc.

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Vol.15 • No. 8 • 2002
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