Almost homoclinic solutions for a certain class of mixed type functional differential equations

• Autorzy: Joanna Janczewska
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 58E50: Applications
• 34K13: Periodic solutions
• 34C37: Homoclinic and heteroclinic solutions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2011
• Tom: 100
• Numer: 1
• Strony: 13-24

Daty

wydano

2011

Twórcy

autor

Joanna Janczewska

• 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

Identyfikatory

DOI

10.4064/ap100-1-2