Topological Methods in Nonlinear Analysis

On the Fučík spectrum for elliptic systems

Eugenio Massa and Bernhard Ruf

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We propose an extension of the concept of Fučík spectrum to the case of coupled systems of two elliptic equations, we study its structure and some applications. We show that near a simple eigenvalue of the system, the Fučík spectrum consists (after a suitable reparametrization) of two (maybe coincident) $2$-dimensional surfaces. Furthermore, by variational methods, parts of the Fučík spectrum which lie far away from the diagonal (i.e. from the eigenvalues) are found. As application, some existence, non-existence and multiplicity results to systems with eigenvalue crossing ("jumping") nonlinearities are proved.

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Topol. Methods Nonlinear Anal., Volume 27, Number 2 (2006), 195-228.

First available in Project Euclid: 13 May 2016

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Massa, Eugenio; Ruf, Bernhard. On the Fučík spectrum for elliptic systems. Topol. Methods Nonlinear Anal. 27 (2006), no. 2, 195--228.

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