Proceedings of the Second ISAAC Congress pp 175-183 | Cite as

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

Chapter

## Abstract

Let Γ
where α=constant> 0,

_{ 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)

*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
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## References

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© Kluwer Academic Publishers 2000