Advances in Differential Equations

Sign changing solutions of nonlinear elliptic equations

Monica Musso and Donato Passaseo

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Abstract

This paper is concerned with a class of nonlinear elliptic Dirichlet problems approximating degenerate equations. If the degeneration set consists of $k$ connected components, by using variational methods, it is proved the existence of $k^{2}$ distinct nodal solutions, having exactly two nodal regions, whose positive and negative parts concentrate near subsets of the degeneration set.

Article information

Source
Adv. Differential Equations, Volume 1, Number 6 (1996), 1025-1052.

Dates
First available in Project Euclid: 25 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1366895243

Mathematical Reviews number (MathSciNet)
MR1409898

Zentralblatt MATH identifier
0864.35044

Subjects
Primary: 35J65: Nonlinear boundary value problems for linear elliptic equations
Secondary: 35B25: Singular perturbations 35J70: Degenerate elliptic equations

Citation

Musso, Monica; Passaseo, Donato. Sign changing solutions of nonlinear elliptic equations. Adv. Differential Equations 1 (1996), no. 6, 1025--1052. https://projecteuclid.org/euclid.ade/1366895243


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Advances in Differential Equations

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