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The Existence of Positive Solutions for Boundary Value Problems for Two Calss of Differential Equation Systems with the Frist Order Derivative

Author: XuYanLing
Tutor: GuoYanPing
School: Hebei University of Science and Technology
Course: Applied Mathematics
Keywords: Ordinary differential equations Boundary value problem Fixed point theorem Conical Quasisymmetric solution Positive solution p Laplacian
CLC: O175.8
Type: Master's thesis
Year: 2012
Downloads: 10
Quote: 0
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Abstract


Differential equations , in the development of science and technology and production practices the has profound practical background , is an integral part of modern science and technology to solve the problem of the tools . In the field of economics , biology , astronomy, physics and other sciences , differential equations have important practical value and significance . Differential equations proposed for the solution of the above problems , has played a very significant results , and provide a corresponding mathematical models in the development process of these practical problems , differential equations , and led to a new area . The differential equations major is to study the existence of solutions of boundary value problems . First to understand the of Differential Equations existence reconciliation number , followed by seeking a numerical solution of the equations . In recent years , nonlinear functional analysis research a lot of the actual value of the mathematical problem and successfully applied in the Boundary Value Problems of studying . This article is a new fixed point theorem and degree theory to discuss the existence of positive solution containing the first derivative of the equations under different boundary conditions . First , to prove the second with p Laplace operator proposed the existence of positive solutions of linear differential equations with multi-point boundary value problem , the use of a new fixed point theorem proving at least one positive solution of the existence of . Second , consider the existence of a class of second-order differential equations with the first derivative of m-point boundary value , once again , through the utilization of theoretical construct containing the first derivative , second-order ordinary differential fixed point theorem proving equations the existence of multi-point boundary value problem Quasisymmetric solution . Finally , by constructing Quasisymmetric operator converts solving fixed point problems , the use of on the structure of the fixed point theorem BVPs quasi - symmetric solution existence conditions .

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