Chornenka O. The asymptotic analysis of the singularly perturbed linear systems of differential equations with the irregular singular point.

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0410U003103

Thesis Registration Form

0410U003103.pdf

Applicant for

Specialization

  • 01.01.02 - Диференційні рівняння

13-04-2010

Specialized Academic Board

Д 26.206.02

The Institute of Mathematics of NASU

Essay

The dissertation research is devoted to construction of the general solution of the singularly perturbed linear system of differential equations with the irregular singular point. It is proved that the asymptotic expansions of these system equations may be constructed as a double series by the fractional degree of parameter and the ratio of the independent variable and parameter. The corresponding equations of branching are deduced and, using the space analogue of the method of Newton's diagrams, these equations are analyzed. The problem of the solutions of nonhomogeneous system in case of the resonance is researched too. Asymptotic character of the formal expansions is studied, the corresponding asymptotic evaluations are found.

Read more

Files

aref.doc

disertation--titull.doc

disertation--ст1.doc

disertation--ст2-8.doc

disertation--ст25-51.doc

disertation--ст52-53.doc

disertation--ст54.doc

disertation--ст55-61.doc

disertation--ст62.doc

disertation--ст63.doc

disertation--ст64-68.doc

disertation--ст69-96.doc

disertation--ст9-24.doc

disertation--ст97-160.doc

Similar theses

0521U102074

Golovaty Yuriy Danylovch

Singularly perturbed differential operators in models of quantum mechanics

0521U101590

Medynsky Ihor Pavlovych

Fundamental solutions of the Cauchy problem for degenerate parabolic equations

0421U102084

Heseleva Kateryna H.

Collocation-Iterative Method for Solving Integro-Functional Equations

0421U102060

Skutar Ihor D.

Asymptotic integration of systems of differential equations with a small parameter at some derivatives.

0421U101723

Myslo Yuliia M.

Asymptotically almost periodic solutions of differential equations with delay and impulses