ISSN:
1618-3932
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In this paper, the concept of generalizedω-periodic solution is given for Riccati's equationy'=a(t)y 2+b(t)y+c(t) with perriodic coefficients, the relation between generalizedω-periodic solutions and the characteristic numbers of systemx'1=c(t)x 2,x'2=−a(t)x 1-b(t)x 2 is indicated, and several necessary and sufficient conditions are given using the coefficients. Moreover, in the case ofa(t) without zero, the relation between the number of continuousω-periodic solutions ofy'=a(t)y 2+b(t)y+c(t)+δ and the parameter δ is given; thus the problem on the existence of continuousω-periodie solutions is basically solved.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02006005
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