A multiplicity result for a class of superquadratic Hamiltonian systems
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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.
CitationMarcos do O, J., & Ubilla, P. (2003). A multiplicity result for a class of superquadratic Hamiltonian systems. Electronic Journal of Differential Equations, 2003(15), pp. 1-14.
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