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Monotone Technique for Periodic Solutions of Differential Equations

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Monotone Technique for Periodic Solutions of Differential Equations

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Title: Monotone Technique for Periodic Solutions of Differential Equations
Author: Leela, S.
Abstract: The existence of periodic solutions has received a great deal of attention in recent years [1,7-11,14]. In [8,11] the existence of solutions of first and second order PBVP (periodic boundary value problem) has been studied successfully by combining the two basic techniques, namely, the method of lower and upper solutions and the Lyapunov-Schmidt method. In [6,11-13] monotone methods are developed for obtaining extremal solutions of BVP as limits of monotone iterates. In the first order PBVP [11] the monotone method has a greater significance since each member of the sequence is a periodic solution of a first order linear equation which can be explicitly computed. In this article, we give a survey of the current state of art of this important method for first and second order PBVP. Our result in [11,13] indicate that this approach is useful to study semilinear parabolic IBVP and other problems at resonance. For the extension of monotone method to finite systems of PBVP, see [15] and to abstract PBVP, see [7].
URI: http://hdl.handle.net/10106/2312
Date: 1982-07

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