An approximative scheme of finding almost homoclinic solutions for a class of Newtonian systems
Keywords
Almost homoclinic solution, periodic orbit, action functional, Newtonian systemAbstract
In this work the problem of the existence of almost homoclinic solutions for a Newtonian system $\ddot{q}+V_{q}(t,q)=f(t)$, where $t\in\mathbb R$ and $q\in\mathbb R^n$, is considered. It is assumed that a potential $V\colon\mathbb R\times\mathbb R^{n}\to\mathbb R$ is $C^{1}$-smooth with respect to all variables and $T$-periodic in a time variable $t$. Moreover, $f\colon\mathbb R\to\mathbb R^{n}$ is a continuous bounded square integrable function and $f\neq 0$. This system may not have a trivial solution. However, we show that under some additional conditions there exists a solution emanating from $0$ and terminating to $0$. We are to call such a solution almost homoclinic to $0$.Downloads
Published
2009-03-01
How to Cite
1.
JANCZEWSKA, Joanna. An approximative scheme of finding almost homoclinic solutions for a class of Newtonian systems. Topological Methods in Nonlinear Analysis. Online. 1 March 2009. Vol. 33, no. 1, pp. 169 - 177. [Accessed 19 April 2024].
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