ON ONE TYPE OF SINGULAR INTEGRAL EQUATIONS.
Abstract
The integral equation a(t) (phi (t) bar) + b(t)/pii multiplied by the integral over L of the quantity (phi(tau)/tau-alpha(t)) d(tau) = c(t) is considered, where a(t), c(t) satisfy Holder's condition on the closed Ljapunov contour L. It is assumed that a(t) and b(t) do not vanish on L. The function alpha(t) is a homeomorphic (direction-preserving) mapping of L upon itself, alpha prime (t) does not equal zero on L and satisfies Holder's condition on L. Under the additional hypotheses that alpha(alpha(t)) = t on L, and a(t) a(alpha(t)) = b(t) b(alpha(t)) on L, the author gives a qualitative analysis of the given integral equation. The number of linearly independent solutions of the homogeneous equation corresponding to (1) is found, and an algorithm is derived for finding these solutions. Conditions for the solvability of Eq. (1) are determined. On the basis of these results the normal solvability and the vanishing of the index of the given integral equation are established. Cases are presented when the given equation can be solved in closed form.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 09, 1967
- Accession Number
- AD0661212
Entities
People
- E. G. Khasobov
- G. S. Litvinchuk
Organizations
- Johns Hopkins University Applied Physics Laboratory