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

Banach Center Publications (2014)

- Volume: 101, Issue: 1, page 107-113
- ISSN: 0137-6934

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topRobert 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 -

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