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On the Existence of Homoclinic Type Solutions of a Class of Inhomogenous Second Order Hamiltonian Systems
Abstract
We show the existence of homoclinic type solutions of a class of inhomogenous second order Hamiltonian systems, where a C1-smooth potential satisfies a relaxed superquadratic growth condition, its gradient is bounded in the time variable, and a forcing term is sufficiently small in the space of square integrable functions. The idea of our proof is to approximate the original system by time-periodic ones, with larger and larger time-periods. We prove that the latter systems admit periodic solutions of mountain-pass type, and obtain homoclinic type solutions of the original system from them by passing to the limit (in the topology of almost uniform convergence) when the periods go to infinity.
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Authors (3)
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Nils Waterstraat
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- Category:
- Articles
- Type:
- artykuły w czasopismach
- Published in:
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Journal of Dynamics and Differential Equations
no. 32,
pages 1343 - 1356,
ISSN: 1040-7294 - Language:
- English
- Publication year:
- 2020
- Bibliographic description:
- Ciesielski J., Janczewska J., Waterstraat N.: On the Existence of Homoclinic Type Solutions of a Class of Inhomogenous Second Order Hamiltonian Systems// Journal of Dynamics and Differential Equations -Vol. 32, (2020), s.1343-1356
- DOI:
- Digital Object Identifier (open in new tab) 10.1007/s10884-019-09774-x
- Sources of funding:
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- Project Morse theoretical methods in Hamiltonian dynamics
- Grant PPP-PL No. 57217076 of DAAD and MNiSW
- Verified by:
- Gdańsk University of Technology
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