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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Multiple solutions of perturbed superquadratic second order Hamiltonian systems


Author: Yi Ming Long
Journal: Trans. Amer. Math. Soc. 311 (1989), 749-780
MSC: Primary 58F05; Secondary 34C25, 58E05, 58E30, 58F22, 70H05
DOI: https://doi.org/10.1090/S0002-9947-1989-0978375-4
MathSciNet review: 978375
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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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Keywords: Classical Hamiltonian system, perturbation, minimax method, <IMG WIDTH="28" HEIGHT="23" ALIGN="BOTTOM" BORDER="0" SRC="images/img7.gif" ALT="${S^1}$"> action, a priori estimates
Article copyright: © Copyright 1989 American Mathematical Society