Differential and Integral Equations

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

Eugenio Massa and Rafael Antônio Rossato

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 18 February 2017

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J57, 49J35


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

Export citation