# Approximative sequences and almost homoclinic solutions for a class of second order perturbed Hamiltonian systems

Marek Izydorek; Joanna Janczewska

Banach Center Publications (2014)

- Volume: 101, Issue: 1, page 87-92
- ISSN: 0137-6934

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topMarek Izydorek, and Joanna Janczewska. "Approximative sequences and almost homoclinic solutions for a class of second order perturbed Hamiltonian systems." Banach Center Publications 101.1 (2014): 87-92. <http://eudml.org/doc/281591>.

@article{MarekIzydorek2014,

abstract = {In this work we will consider a class of second order perturbed Hamiltonian systems of the form $q̈ + V_q(t,q) = f(t)$, where t ∈ ℝ, q ∈ ℝⁿ, with a superquadratic growth condition on a time periodic potential V: ℝ × ℝⁿ → ℝ and a small aperiodic forcing term f: ℝ → ℝⁿ. To get an almost homoclinic solution we approximate the original system by time periodic ones with larger and larger time periods. These approximative systems admit periodic solutions, and an almost homoclinic solution for the original system is obtained from them by passing to the limit in $C²_\{loc\}(ℝ,ℝⁿ)$ when the periods go to infinity. Our aim is to show the existence of two different approximative sequences of periodic solutions: one of mountain pass type and the second of local minima.},

author = {Marek Izydorek, Joanna Janczewska},

journal = {Banach Center Publications},

keywords = {almost homoclinic solution; approximative method; critical point; Hamiltonian system},

language = {eng},

number = {1},

pages = {87-92},

title = {Approximative sequences and almost homoclinic solutions for a class of second order perturbed Hamiltonian systems},

url = {http://eudml.org/doc/281591},

volume = {101},

year = {2014},

}

TY - JOUR

AU - Marek Izydorek

AU - Joanna Janczewska

TI - Approximative sequences and almost homoclinic solutions for a class of second order perturbed Hamiltonian systems

JO - Banach Center Publications

PY - 2014

VL - 101

IS - 1

SP - 87

EP - 92

AB - In this work we will consider a class of second order perturbed Hamiltonian systems of the form $q̈ + V_q(t,q) = f(t)$, where t ∈ ℝ, q ∈ ℝⁿ, with a superquadratic growth condition on a time periodic potential V: ℝ × ℝⁿ → ℝ and a small aperiodic forcing term f: ℝ → ℝⁿ. To get an almost homoclinic solution we approximate the original system by time periodic ones with larger and larger time periods. These approximative systems admit periodic solutions, and an almost homoclinic solution for the original system is obtained from them by passing to the limit in $C²_{loc}(ℝ,ℝⁿ)$ when the periods go to infinity. Our aim is to show the existence of two different approximative sequences of periodic solutions: one of mountain pass type and the second of local minima.

LA - eng

KW - almost homoclinic solution; approximative method; critical point; Hamiltonian system

UR - http://eudml.org/doc/281591

ER -

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