Differential and Integral Equations

Three solutions for an elliptic system near resonance with the principal eigenvalue

Eugenio Massa and Rafael Antônio Rossato

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Abstract

We consider an elliptic system of Hamiltonian type with linear part depending on two parameters and a sublinear perturbation. We obtain the existence of at least three solutions when the linear part is near resonance with the principal eigenvalue, either from above or from below. For two of these solutions, we also obtain information on the sign of its components. The system is associated to a strongly indefinite functional and the solutions are obtained trough saddle point theorem, after truncating the nonlinearity.

Article information

Source
Differential Integral Equations, Volume 30, Number 3/4 (2017), 207-230.

Dates
First available in Project Euclid: 18 February 2017

Permanent link to this document
https://projecteuclid.org/euclid.die/1487386823

Mathematical Reviews number (MathSciNet)
MR3611499

Zentralblatt MATH identifier
06738548

Subjects
Primary: 35J57, 49J35

Citation

Massa, Eugenio; Rossato, Rafael Antônio. Three solutions for an elliptic system near resonance with the principal eigenvalue. Differential Integral Equations 30 (2017), no. 3/4, 207--230. https://projecteuclid.org/euclid.die/1487386823


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