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Abstrakty
We shall be concerned with the existence of almost homoclinic solutions for a class of second order functional differential equations of mixed type: $q̈(t)+V_{q}(t,q(t))+u(t,q(t),q(t-T),q(t+T)) = f(t)$, 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.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
13-24
Opis fizyczny
Daty
wydano
2011
Twórcy
autor
- Faculty of Technical Physics and Applied Mathematics, Gdańsk University of Technology, Narutowicza 11/12, 80-233 Gdańsk, Poland
- Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa, Poland
Bibliografia
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_4064-ap100-1-2