Dissertation > Excellent graduate degree dissertation topics show

Differential Inequalities and Singularly Perturbated Phenomenon

Author: FuYangGeng
Tutor: ZhouZheYanï¼›YuZanPing
School: Fujian Normal University
Course: Basic mathematics
Keywords: Differential Equations Differential system Edge value to the title Nagumo condition Singular perturbation Differential inequality TURNING POINT High-end expand
CLC: O175.8
Type: Master's thesis
Year: 2008
Downloads: 59
Quote: 1
Read: Download Dissertation

Abstract


In this paper, the use of differential inequality techniques ( otherwise known as the upper and lower solution method ) , prove that a class of nonlinear differential equations ( without parameters) ( part of the contents of the existence of solutions including the uniqueness of solution ) under certain conditions , this with a few of the small parameter singularly perturbed boundary value problems, boundary layer function method to construct higher order asymptotic solution to obtain the uniformly valid estimated ; study on the basis of a class does not satisfy the Nagumo condition differential system boundary value problems of the theory of differential inequalities . The paper is divided into four chapters : the first chapter , the first to introduce a singular perturbation theory background and previous work . Second, given the concept of lower and upper solutions and Nagumo condition , while the basic results of the second-order differential inequality , and the basic lemma will be used later . Chapter II , the use of upper and lower solution method to study the existence and uniqueness of a turning point third-order differential equation boundary value problem solution and construct higher order asymptotic expansion , then the use of the third-order differential inequality theory to calculate understanding of high-order error estimates . The third chapter , the use of upper and lower solutions , study a class of two-point boundary value problems for second-order differential system theory of differential inequality to obtain that there exists a unique - theorem ; Lyapunov function to study differential system and those above the boundary value problem of differential inequality theory . Chapter IV , using the theory of differential inequalities exist only for a class of second order differential equations periodic Boundary Value Problems - Sexual and its extension into differential equations periodic solution under certain conditions , the last study of its singular perturbation .

Related Dissertations

  1. Convergence and Stability of Numerical Solution of Stochastic Differential Equations with Piecewise Continuous Arguments,O211.63
  2. Research on Data Acquisition and Processing Methods for Weapon Evaluation System,TJ06
  3. On the Risk Model Involving Two Classes of Claims with Threshold Dividend Strategy,O211.67
  4. Fractional Differential resonance boundary value problems,O175.8
  5. Spectral Method for Solving Two Types of Delay Differential Equations,O241.8
  6. Takens-Bogdanov Bifurctaions in Differential Equations with Two Delays,O175
  7. Contrast Relation in Academic Journal Articles,H314
  8. The Existence of Global Solution for Stochastic Functional Differential Equation,O211.63
  9. The Existence of Positive Solutions of a Class of Even Order Nonlinear Differential Equations,O175
  10. Algorithem Research to Obtain Symmetry Group for Two Types of Soliton Equations Based on Symbolic Compution,O241.8
  11. A Class of Collocation Methods for Second Order Ordinary Differential Equation,O175.1
  12. The Numerical Solution of BVPs for a Class of Functional Differential Equations,O175.8
  13. Delay differential equations stability,O241.8
  14. Blowup noise suppression and the impact on the dynamic behavior,O211.63
  15. Non- local Higher Order Differential Equations Boundary Value Existence,O175.8
  16. About ODE (k, nk) conjugate boundary value problems,O175.8
  17. The Existence of Positive Solutions for Boundary Value Problems for Two Calss of Differential Equation Systems with the Frist Order Derivative,O175.8
  18. Based on variational level set image segmentation algorithm,TP391.41
  19. PDE-based image denoising and enhancement of,TP391.41
  20. Image restoration of key technologies,TP391.41
  21. PDE-based image registration and fusion method,TP391.41

CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Boundary Value Problems
© 2012 www.DissertationTopic.Net  Mobile