TY  - JOUR
A1  - Kloeden, Peter E.
A1  - Krasnoselʹskij, Alexander M.
T1  - Periodic solutions of systems with asymptotically even nonlinearities
T2  - Journal of applied mathematics and stochastic analysis
N2  - 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.
KW  - Index at Infinity
KW  - Degenerate Linear Part
KW  - Asymptotically Even Nonlinearity
KW  - Boundary Value Problems
Y1  - 2000
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/8117
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30-80657
SN  - 1048-9533
N1  - 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.
VL  - vol. 13 (2000)
IS  - Issue 1
SP  - 41
EP  - 50
PB  - Hindawi
CY  - New York, NY
ER  -