A convergence result for mountain pass periodic solutions of perturbed Hamiltonian systems

被引:1
|
作者
Izydorek, Marek [1 ]
Janczewska, Joanna [1 ]
Soares, Pedro [2 ]
机构
[1] Gdansk Univ Technol, Fac Appl Phys & Math, Inst Appl Math, Narutowicza 11-12, PL-80233 Gdansk, Poland
[2] Univ Lisbon, Anal & Matemat Financeira, ISEG Lisbon Sch Econ & Management, Rua Quelhas 6, P-1200781 Lisbon, Portugal
关键词
Mountain pass lemma; periodic solution; perturbation problem; Hamiltonian system; variational method;
D O I
10.1142/S0219199722500110
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this work, we study second-order Hamiltonian systems under small perturbations. We assume that the main term of the system has a mountain pass structure, but do not suppose any condition on the perturbation. We prove the existence of a periodic solution. Moreover, we show that periodic solutions of perturbed systems converge to periodic solutions of the unperturbed systems if the perturbation tends to zero. The assumption on the potential that guarantees the mountain pass geometry of the corresponding action functional is of independent interest as it is more general than those by Rabinowitz [Homoclinic orbits for a class of Hamiltonian systems, Proc. R. Soc. Edinburgh A 114 (1990) 33-38] and the authors [M. Izydorek and J. Janczewska, Homoclinic solutions for a class of the second-order Hamiltonian systems, J. Differ. Equ. 219 (2005) 375-389].
引用
收藏
页数:10
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