On singular integral equations with variable limits of integration

Abstract

The wide range of problems of mathematical physics is reduced to a special Volterra integral equation of the second kind or to integral equations with variable limits of integration. Among such problems we can include: boundary value problems for spectrally loaded differential equations [1–4], inverse problems [5, 6], nonlocal problems [7], boundary value problems for domains with moving boundaries as the domain degenerates at the time [8, 9] and others. In the study of integral equations with a variable lower limit of integration, the operational method can not be used directly, since in this case the convolution theorem is not applicable. However, the Laplace transform can be used to study this kind of integral equation by applying the method of model solutions.