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

Joanna Janczewska. "Almost homoclinic solutions for a certain class of mixed type functional differential equations." Annales Polonici Mathematici 100.1 (2011): 13-24. <http://eudml.org/doc/280399>.

@article{JoannaJanczewska2011,
abstract = {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.},
author = {Joanna Janczewska},
journal = {Annales Polonici Mathematici},
keywords = {mixed-type functional differential equation; almost homoclinic solutions; variational methods},
language = {eng},
number = {1},
pages = {13-24},
title = {Almost homoclinic solutions for a certain class of mixed type functional differential equations},
url = {http://eudml.org/doc/280399},
volume = {100},
year = {2011},
}

TY - JOUR
AU - Joanna Janczewska
TI - Almost homoclinic solutions for a certain class of mixed type functional differential equations
JO - Annales Polonici Mathematici
PY - 2011
VL - 100
IS - 1
SP - 13
EP - 24
AB - 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.
LA - eng
KW - mixed-type functional differential equation; almost homoclinic solutions; variational methods
UR - http://eudml.org/doc/280399
ER -