Multiple solutions of perturbed superquadratic second order Hamiltonian systems

Long, Yi Ming

doi:10.1090/S0002-9947-1989-0978375-4

Multiple solutions of perturbed superquadratic second order Hamiltonian systems
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Trans. Amer. Math. Soc. 311 (1989), 749-780 Request permission

Abstract:

In this paper we prove the existence of infinitely many distinct $T$-periodic solutions for the perturbed second order Hamiltonian system $\ddot q + V’(q) = f(t)$ under the conditions that $V:{{\mathbf {R}}^N} \to {\mathbf {R}}$ is continuously differentiable and superquadratic, and that $f$ is square integrable and $T$-periodic. In the proof we use the minimax method of the calculus of variation combining with a priori estimates on minimax values of the corresponding functionals.

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