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On the Existence of Periodic Solutions for the Quasi-Linear Third-Order Differential Equation

โœ Scribed by B Mehri; M Niksirat

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
81 KB
Volume
261
Category
Article
ISSN
0022-247X

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โœฆ Synopsis

In this paper we consider the nonlinear third-order quasi-linear differential equation

and obtain some simple conditions for the existence of a periodic solution for it. In so doing we use the implicit function theorem to prove a theorem about the existence of periodic solutions and consider one example to show the realizability of the conditions. The validity of the conditions for the parameter-free problem x + k 2 x = f x x x also is considered.

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## Abstract In this paper, we establish several criteria for the existence, multiplicity, nonexistence of positive periodic solutions of the following system by combining some new properties of Green's function together with Krasnosel'skฤญ fixed point theorem on the compression and expression of co