Periodic solutions of systems with asymptotically even nonlinearities

  • New conditions of solvability based on a general theorem on the calculation of the index at infinity for vector fields that have degenerate principal linear part as well as degenerate ... next order ... terms are obtained for the 2 Pi-periodic problem for the scalar equation x'' +n2x=g(|x|)+f(t,x)+b(t) with bounded g(u) and f(t,x) -> 0 as |x| -> 0. The result is also applied to the solvability of a two-point boundary value problem and to resonant problems for equations arising in control theory. AMS subject classifications: 47Hll, 47H30.

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Author:Peter E. Kloeden, Alexander M. Krasnoselʹskij
Parent Title (English):Journal of applied mathematics and stochastic analysis
Place of publication:New York, NY
Document Type:Article
Date of Publication (online):2010/09/24
Year of first Publication:2000
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2010/09/24
Tag:Asymptotically Even Nonlinearity; Boundary Value Problems; Degenerate Linear Part; Index at Infinity
Volume:vol. 13 (2000)
Issue:Issue 1
Page Number:10
First Page:41
Last Page:50
Copyright © 2000 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Institutes:Informatik und Mathematik / Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):License LogoDeutsches Urheberrecht