Advances in Differential Equations

Sign changing solutions of nonlinear elliptic equations

Monica Musso and Donato Passaseo

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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

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

First available in Project Euclid: 25 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


Musso, Monica; Passaseo, Donato. Sign changing solutions of nonlinear elliptic equations. Adv. Differential Equations 1 (1996), no. 6, 1025--1052.

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