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Periodic solutions of equations with oscillating nonlinearities

✍ Scribed by A.M. Krasnosel'skii; J. Mawhin

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
754 KB
Volume
32
Category
Article
ISSN
0895-7177

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✦ Synopsis

In

this paper, we consider the Sn-periodic problem for the equation

where n is a positive integer, b(t) is continuous and Pn-periodic, and f(x) is bounded and continuous. We give a new formulation for the Lazer-Leach conditions for the existence of 2a-periodic solutions, and new sufficient conditions for the existence of unbounded sequences of such solutions.

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We study uniqueness and stability problems of slowly oscillating periodic solutions of delay equations with sinall parameters. If the nonlinearity decays to a negative number at \(-\infty\) and blows up at \(+\infty\) or vice versa, we show that, for sufficiently small parameters, the slowly oscilla