A multiplicity result for a class of superquadratic Hamiltonian systems

• Main Authors: Joao Marcos Do O, Pedro Ubilla
• Format: Article
• Language: English
• Published: Texas State University 2003-02-01
• Series: Electronic Journal of Differential Equations
• Subjects: Elliptic systems; minimax techniques; Mountain Pass Theorem; Ekeland's variational principle
• Online Access: http://ejde.math.txstate.edu/Volumes/2003/15/abstr.html

We establish the existence of two nontrivial solutions to semilinear elliptic systems with superquadratic and subcritical growth rates. For a small positive parameter $ lambda $, we consider the system $$displaylines{ -Delta v = lambda f(u) quad hbox{in } Omega , cr -Delta u = g(v) quad hbox{in } Omega , cr u = v=0 quad hbox{on } partial Omega , }$$ where $Omega$ is a smooth bounded domain in $mathbb{R}^N$ with $Ngeq 1$. One solution is obtained applying Ambrosetti and Rabinowitz's classical Mountain Pass Theorem, and the other solution by a local minimization. end{abstract}