Accession Number : AD0661212

Title :   ON ONE TYPE OF SINGULAR INTEGRAL EQUATIONS.

Descriptive Note : APL library bulletin translations series,

Corporate Author : JOHNS HOPKINS UNIV SILVER SPRING MD APPLIED PHYSICS LAB

Personal Author(s) : Litvinchuk,G. S. ; Khasobov,E. G.

Report Date : 09 FEB 1967

Pagination or Media Count : 28

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.

Descriptors :   (*INTEGRAL EQUATIONS, PROBLEM SOLVING), MAPPING(TRANSFORMATIONS), ALGORITHMS, BOUNDARY VALUE PROBLEMS, COMPLEX VARIABLES, THEOREMS, USSR

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE