ON ONE TYPE OF SINGULAR INTEGRAL EQUATIONS.
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JOHNS HOPKINS UNIV SILVER SPRING MD APPLIED PHYSICS LAB
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The integral equation at phi t bar btpii multiplied by the integral over L of the quantity phitautau-alphat dtau ct is considered, where at, ct satisfy Holders condition on the closed Ljapunov contour L. It is assumed that at and bt do not vanish on L. The function alphat is a homeomorphic direction-preserving mapping of L upon itself, alpha prime t does not equal zero on L and satisfies Holders condition on L. Under the additional hypotheses that alphaalphat t on L, and at aalphat bt balphat 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.
- Theoretical Mathematics