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Solutions with minimal period for Hamiltonian systems in a potential well. (English) Zbl 0623.58013

Let \(U\in C^ 2(\Omega)\), where \(\Omega\) is a bounded set in \({\mathbb{R}}^ N\). Suppose that U(x) tends to \(+\infty\) as x tends to \(\partial \Omega\). Our main results concern the existence of periodic solutions of - ẍ\(=U'(x)\) having a prescribed number T as minimal period. The results are also generalized to first order Hamiltonian systems.

MSC:

37G99 Local and nonlocal bifurcation theory for dynamical systems
49J35 Existence of solutions for minimax problems
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References:

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