Elliptic systems of Hamiltonian type near resonance

Author(s)

Rafael Antonio Rossato

• Document type: Doctoral Thesis
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2014-10-30

Examining board members

Eugenio Tommaso Massa; Francisco Odair Vieira de Paiva; Leonelo Patricio Iturriaga Pastene; Sérgio Henrique Monari Soares; Marco Aurélio Soares Souto

• Advisor: Eugenio Tommaso Massa

Abstract

In this work we consider elliptic systems of hamiltonian type, involving the Laplacian operator, a linear part depending on two parameters and a sublinear perturbation. We obtain the existence of at least two solutions when the linear part is near resonance (this phenomenon is called almost-resonance). We also show the existence of a third solution when the almost-resonance is with respect to the first eigenvalue of the Laplacian operator. In the resonant case, we obtain similar results, with an additional sublinear term. These systems are associated with strongly indefinite functionals, and the solutions are obtained by Saddle Point Theorem and Galerkin approximation. (AU)

• FAPESP's process: 10/06411-4 - variational characterization of the Fucik spectrum and applications
• Grantee: Rafael Antônio Rossato
• Support Opportunities: Scholarships in Brazil - Doctorate