Advertisement

Linear Conjugate Boundary Value Problems for First Order Ordinary System of Linear Differential Equations with Singular or Super Singular Coefficients

  • Nusrat Rajabov
Part of the International Society for Analysis, Applications and Computation book series (ISAA, volume 7)

Abstract

Let Γ o = {0 < x < b} be a set of the point on the real axis, containing the point x = c, 0 < c < b. In Γ = Γ o\{c} we consider the following first order linear system
$$ {\left| {x - c} \right|^\alpha }Y_j^\prime (x) + \sum\limits_{k = 1}^2 {{P_{jk}}} (x){Y_k}(x) = {f_j}(x),j = 1,2, $$
(1)
where α=constant> 0, P jk (x), f j (x) (j, k = 1, 2) are given functions in Γ with first genus singularity at x = c. The problem is to find a manifold solution in term of arbitrary constant and investigations of boundary valued problems, for the first order ordinary differential equation and first order ordinary system of differential equations with singular or super-singular points and its application, which has been studied in [1]–[9].

Keywords

Integral Operator Integral Representation Arbitrary Constant Linear Differential Equation Algebraic System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Rajabov N., Integral representation and boundary value problems for some differential equations with singular lines or singular surfaces (Introduction in the theory nonmodel the second order hyperbolic equation with singular lines), part 4 (Russian), Tajik State University Publishers, Dushanbe, 1985, 147 pp.Google Scholar
  2. [2]
    Rajabov N., Linear hyperbolic equations with two singular lines. Integral equations and boundary value problems. World Scientific, Singapore, New-Jersey, London, Hong-Kong, 1991, 170–175.Google Scholar
  3. [3]
    Rajabov N., Linear hyperbolic equations of the fourth order with two singular lines. Proceeding of Asian Mathematical Conference, 1990 (Hong-Kong, 1990), World Scientific, 1992, 387–393.Google Scholar
  4. [4]
    Rajabov N., The system two first order ordinary differential equation with super-singular points. Proceedings of international scientific conference on differential equations with singular coefficients, 1996 (Dushanbe, 1996 ), 69.Google Scholar
  5. [5]
    Rajabov N. and Mirzoev A. M., Cauchy type problems for the two first order system ordinary linear differential equation with one super-singular point. Proceedings of international scientific conference on differential equations with singular coefficients, 1996 (Dushanbe, 1996 ), 71.Google Scholar
  6. [6]
    Rajabov N. and Chojaev S., To theory of the one class two first order system ordinary differential equation with one super-singular point. Proceedings of international scientific conference on differential equations with singular coefficients, 1996 (Dushanbe, 1996 ), 74.Google Scholar
  7. [7]
    Rajabov N., Linear conjugate boundary value problem for the two second order linear ordinary differential equation with super-singular coefficients. ICM 1998, International Congress of Mathematicians (Berlin, August 18–27, 1998, Abstracts of Short Communications and Poster Sessions), 186.Google Scholar
  8. [8]
    Rajabov N., An introduction to the theory of partial differential equations with super-singular coefficients (forsi), Tehran University Publishers, Tehran, 1996, 230 p.Google Scholar
  9. [9]
    Rajabov N., Introduction to ordinary differential equation with super-singular coefficients ( English ), Dushanbe, 1998, 160 p.Google Scholar
  10. [10]
    Gachov F. D., Boundary value problems, “Nauka”, M., 1977, 640 p.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Nusrat Rajabov
    • 1
  1. 1.Tajik State National UniversityDushanbeTajikistan

Personalised recommendations