A note on an approximative scheme of finding almost homoclinic solutions for Newtonian systems

Robert Krawczyk. "A note on an approximative scheme of finding almost homoclinic solutions for Newtonian systems." Banach Center Publications 101.1 (2014): 107-113. <http://eudml.org/doc/281955>.

@article{RobertKrawczyk2014,
abstract = {In this work we will be concerned with the existence of almost homoclinic solutions for a Newtonian system $q̈ + ∇_\{q\}V(t,q) = f(t)$, where t ∈ ℝ, q ∈ ℝⁿ. It is assumed that a potential V: ℝ × ℝⁿ → ℝ is C¹-smooth and its gradient map $∇_\{q\}V: ℝ × ℝⁿ → ℝⁿ$ is bounded with respect to t. Moreover, a forcing term f: ℝ → ℝⁿ is continuous, bounded and square integrable. We will show that the approximative scheme due to J. Janczewska (see [J2]) for a time periodic potential extends to our case.},
author = {Robert Krawczyk},
journal = {Banach Center Publications},
keywords = {almost homoclinic solution; approximative method; Newtonian system},
language = {eng},
number = {1},
pages = {107-113},
title = {A note on an approximative scheme of finding almost homoclinic solutions for Newtonian systems},
url = {http://eudml.org/doc/281955},
volume = {101},
year = {2014},
}

TY - JOUR
AU - Robert Krawczyk
TI - A note on an approximative scheme of finding almost homoclinic solutions for Newtonian systems
JO - Banach Center Publications
PY - 2014
VL - 101
IS - 1
SP - 107
EP - 113
AB - In this work we will be concerned with the existence of almost homoclinic solutions for a Newtonian system $q̈ + ∇_{q}V(t,q) = f(t)$, where t ∈ ℝ, q ∈ ℝⁿ. It is assumed that a potential V: ℝ × ℝⁿ → ℝ is C¹-smooth and its gradient map $∇_{q}V: ℝ × ℝⁿ → ℝⁿ$ is bounded with respect to t. Moreover, a forcing term f: ℝ → ℝⁿ is continuous, bounded and square integrable. We will show that the approximative scheme due to J. Janczewska (see [J2]) for a time periodic potential extends to our case.
LA - eng
KW - almost homoclinic solution; approximative method; Newtonian system
UR - http://eudml.org/doc/281955
ER -