Skip to main content
Kent Academic Repository

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. (KAR id:65033)

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: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Nils Waterstraat
Date Deposited: 06 Dec 2017 14:09 UTC
Last Modified: 09 Dec 2022 19:52 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/65033 (The current URI for this page, for reference purposes)

University of Kent Author Information

Waterstraat, Nils.

Creator's ORCID:
CReDIT Contributor Roles:
  • Depositors only (login required):

Total unique views for this document in KAR since July 2020. For more details click on the image.