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On the existence of homoclinic type solutions of a class of inhomogenous second order Hamiltonian systems

Ciesielski, Jakub, Janczewska, Joanna, Waterstraat, Nils (2017) On the existence of homoclinic type solutions of a class of inhomogenous second order Hamiltonian systems. Differential Integral Equations, 30 (3/4). pp. 259-272. ISSN 0893-4983.

Abstract

We study the existence of homoclinic type solutions for second order Lagrangian systems of the type \(q̈(t)-q(t)+a(t)\nabla G(q(t))=f(t)\), where \(t\) \(\varepsilon\) \(\Bbb R\), \(q\) \(\varepsilon\) \(\Bbb R^n\), \(a:\Bbb R \longrightarrow \Bbb R^n\) is a continuous positive bounded function, \(G: \Bbb R^n \longrightarrow \Bbb R\) is a \(C^1\)-smooth potential satisfying the Ambrosetti-Rabinowitz superquadratic growth condition and \(f:\Bbb R \longrightarrow \Bbb R^n\) is a continuous bounded square integrable forcing term. A homoclinic type solution is obtained as limit of \(2k\)-periodic solutions of an approximative sequence of second order differential equations.

Item Type: Article
Subjects: Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus
Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics
Depositing User: Nils Waterstraat
Date Deposited: 06 Dec 2017 14:09 UTC
Last Modified: 07 Feb 2020 11:40 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/65033 (The current URI for this page, for reference purposes)
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