In this work we will be concerned with the existence of almost homoclinic solutions for a Newtonian system , where t ∈ ℝ, q ∈ ℝⁿ. It is assumed that a potential V: ℝ × ℝⁿ → ℝ is C¹-smooth and its gradient map is bounded with respect to t. Moreover, a forcing term f: ℝ → ℝⁿ is continuous, bounded and square integrable. We will show that the approximative scheme due to J. Janczewska (see [J2]) for a time periodic potential extends to our case.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc101-0-8,
author = {Robert Krawczyk},
title = {A note on an approximative scheme of finding almost homoclinic solutions for Newtonian systems},
journal = {Banach Center Publications},
volume = {102},
year = {2014},
pages = {107-113},
zbl = {1300.34097},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc101-0-8}
}
Robert Krawczyk. A note on an approximative scheme of finding almost homoclinic solutions for Newtonian systems. Banach Center Publications, Tome 102 (2014) pp. 107-113. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc101-0-8/