A multiplicity result for a class of superquadratic Hamiltonian systems
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Date
2003-02-14
Authors
do O, Joao Marcos
Ubilla, Pedro
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
We establish the existence of two nontrivial solutions to semilinear elliptic systems with superquadratic and subcritical growth rates. For a small positive parameter λ, we consider the system
-∆v = λƒ(u) in Ω,
-∆u = g(v) in Ω,
u = v = 0 on ∂Ω,
where Ω is a smooth bounded domain in ℝN with N ≥ 1. One solution is obtained applying Ambrosetti and Rabinowitz's classical Mountain Pass Theorem, and the other solution by a local minimization.
Description
Keywords
Elliptic systems, Minimax techniques, Mountain Pass Theorem, Ekeland's variational principle, Multiplicity of solutions
Citation
Marcos do O, J., & Ubilla, P. (2003). A multiplicity result for a class of superquadratic Hamiltonian systems. <i>Electronic Journal of Differential Equations, 2003</i>(15), pp. 1-14.
Rights
Attribution 4.0 International