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Research on the Positive Solutions of BVP and Anti-periodic Solutions for Functional Differential Equations

Author: JiaBaoRui
Tutor: ZhouZongFu
School: Anhui University
Course: Basic mathematics
Keywords: Nonlinear Functional Differential Equations Boundary Value Problems Order Neutral Distributed Delays Anti- periodic solutions Fixed point theory Coincidence degree theory Fractional Positive Solutions
CLC: O175.8
Type: Master's thesis
Year: 2011
Downloads: 49
Quote: 0
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Abstract


Differential Equations is abstracted from the problem from the actual description of the mathematical model of the phenomenon of delay , it is widely used in biology , physics, control theory and engineering problems . Consequently, research Functional Differential Equations , issues such as anti- periodic solutions of great significance . Moreover, as the new hotspot , fractional Differential Equations in various fields, also has a wide range of applications , therefore , depth nonlinear Fractional Differential Equation Boundary Value Problems of a wide range of theoretical and practical significance . this paper mainly discusses nonlinear Functional Differential Equations , anti- periodic solutions for problems and fractional Differential Equations Boundary Value problems existence text is divided into four chapters , the main contents as follows : The first chapter introduces the relevant functional differential equation boundary value problems and counter-cyclical fractional differential equations as well as an overview of the development of this major work . chapter studied p-Laplace operator with a third-order non- linear Functional Differential Equations , by means of Avery-Peterson fixed point theorem and some analysis techniques , the presence of multiple positive solutions are given sufficient conditions for the third chapter , the use of coincidence degree theory, a reasoning and analytical skills to discuss a class with Distributed Delays order Neutral Functional Differential anti- existence and uniqueness of periodic solutions for the problem in the problem , the project 's coefficient c (t) depends on t, which in the past did not appear in the literature before. Moreover, the conclusion of this chapter concise, easy to verify that Chapter IV , with the tensile and compression cone fixed point theorem , to explore and nonlinear terms are given in the case of a singular point , three fractional differential equations point boundary value problem on more than one sufficient condition for existence of positive solutions .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Boundary Value Problems
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