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

• Autorzy: Robert Krawczyk
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 70H05: Hamilton's equations
• 34C37: Homoclinic and heteroclinic solutions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2014
• Tom: 101
• Numer: 1
• Strony: 107-113

Daty

wydano

2014

Twórcy

autor

Robert Krawczyk

• Faculty of Applied Physics and Mathematics, Gdańsk University of Technology, G. Narutowicza 11/12, 80-233 Gdańsk, Poland

Identyfikatory

DOI

10.4064/bc101-0-8