On existence of infinitely many homoclinic solutions

Authors
Wojcik, K Zgliczynski, P
Citation
K. Wojcik et P. Zgliczynski, On existence of infinitely many homoclinic solutions, MONATS MATH, 130(2), 2000, pp. 155-160
Citations number
12
Categorie Soggetti
Mathematics
Journal title
MONATSHEFTE FUR MATHEMATIK
ISSN journal
00269255 → ACNP
Volume
130
Issue
2
Year of publication
2000
Pages
155 - 160
Database
ISI
SICI code
0026-9255(2000)130:2<155:OEOIMH>2.0.ZU;2-N
Abstract
In this note we prove some sufficient condition for the existence of homocl inic solutions in nonautonomous ODE's. As an application we show that there exist infinitely many (geometrically distinct) homoclinic solutions to the trivial 0 solution in the planar system z = (Z) over bar(1 + E-ikt\z\(2)) for 0 < kappa sufficiently small. 1991 Mathematics Subject Classification: 34C35, 34C25, 58F22.