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• # Artykuł - szczegóły

## Annales Polonici Mathematici

2011 | 100 | 1 | 13-24

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

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.

13-24

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