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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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Category:
Articles
Type:
artykuły w czasopismach
Published in:
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
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Gdańsk University of Technology

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