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Existence of Positive Solutions of Dynamic Equations on for Boundary Problems and Periodic Boundary Problems on Time Scales

Author: ZhangBo
Tutor: YangJun
School: Yanshan University
Course: Computational Mathematics
Keywords: Time scale Dynamic equation Eigenvalue Positive solution Boundary value problem Periodic Boundary Value Problems
CLC: O175.8
Type: Master's thesis
Year: 2010
Downloads: 15
Quote: 0
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Abstract


With the development of modern science and technology in a wide range of disciplines in the natural and social sciences , it has proposed a large number of differential equations and difference equations . After differencing , the differential equation leads to a differential equation , many properties of differential equations is retained after differencing , but a lot of examples show that between the two , there are many different nature . The time scale theory calculations include both differential and differential and unify , which pioneered the emerging research topics of the power equation . On the one hand this is because dynamic equations on a time scale of differential equations and difference equations as its special case , and thus help to reveal the nature of the continuous and discrete systems , to avoid duplication of similar results proved ; the other hand , R in addition to the set of real numbers , the set of integers , there are many interesting time scale exist. Therefore, the study of this theory is an important theoretical and practical significance . In addition, the dynamic equations on time scales is a relatively new branch of applied mathematics has a broad application prospects . Applications , the dynamic equations extensive factual basis , such as in the insect population models , neural network model , thermal conductivity , and infectious disease model in will power equation . In addition to biological applications , this mathematical tool has also been used to improve the computing model of the stock market . On the basis of the existing theory of time scale , the thesis marked with several dynamic equation boundary value problem , the Boundary Value existence in the cycle were studied . First, we discuss the existence of solutions of a class of second-order dynamic equation two - point boundary value problems in the time scale , the use of the Green's function and Krasnoselskii fixed point theorem eigenvalue interval of the existence of positive solutions . Second , consider the existence of positive solutions to the three-point boundary value problem of the two types of third - order dynamic equations on time scale to obtain a sufficient condition of the existence of positive solutions . Finally, the time scale on the order nonlinear dynamic equations with constant cycle Boundary Value existence .

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