We shall be concerned with the existence of almost homoclinic solutions for a class of second order functional differential equations of mixed type: , where t ∈ ℝ, q ∈ ℝⁿ and T>0 is a fixed positive number. By an almost homoclinic solution (to 0) we mean one that joins 0 to itself and q ≡ 0 may not be a stationary point. We assume that V and u are T-periodic with respect to the time variable, V is C¹-smooth and u is continuous. Moreover, f is non-zero, bounded, continuous and square-integrable. The main result provides a certain approximative scheme of finding an almost homoclinic solution.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap100-1-2,
author = {Joanna Janczewska},
title = {Almost homoclinic solutions for a certain class of mixed type functional differential equations},
journal = {Annales Polonici Mathematici},
volume = {101},
year = {2011},
pages = {13-24},
zbl = {1221.34176},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap100-1-2}
}
Joanna Janczewska. Almost homoclinic solutions for a certain class of mixed type functional differential equations. Annales Polonici Mathematici, Tome 101 (2011) pp. 13-24. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap100-1-2/