# 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 Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, CalculusQ Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations Faculties > Sciences > School of Mathematics Statistics and Actuarial ScienceFaculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics Nils Waterstraat 06 Dec 2017 14:09 UTC 07 Feb 2020 11:40 UTC https://kar.kent.ac.uk/id/eprint/65033 (The current URI for this page, for reference purposes)