Pairs of Positive Periodic Solutions of Second Order Nonlinear Equations

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Fattahpour, Haniyeh | 2013

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 44537 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Hesaaraki, Mahmoud
Abstract:
In this thesis we study the problem of existence and multiplicity of positive periodic solution to the scalar ODE , , where is a positive function on , super linear at zero and sub linear at infinity, and is a -periodic and sign indefinite weight with negative mean value. We first show the nonexistence of solution for some classes of nonlinearities when is small. Then, using critical point theory, we prove the existence of at least two positive -periodic solutions for large. Then, we prove the existence of a pair of positive -periodic solutions as well as the existence of positive sub harmonic solutions of any order for the scalar second order ODE where is same as above, and is a -periodic and sign indefinite weight of the form , with and large
Keywords:
Critical Point ; Poincare Map ; Positive Periodic Solutions ; Necessary Conditions ; Positive Solutions Pairs ; Subharmonics

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