Regularized Asymptotic Solutions of a Singularly Perturbed Fredholm Equation with a Rapidly Varying Kernel and a Rapidly Oscillating Inhomogeneity

This article investigates an equation with a rapidly oscillating inhomogeneity and decreasing kernel of integral operator Fredholm type. Earlier, differential problems this type were studied in which the term was either absent or had form Volterra-type integral. The presence its significantly affect development algorithm for asymptotic solutions, implementation it is necessary to take into account essential singularities generated by operator. It shown tise work that when passing structure essentially singular changes from Volterra If case they change independent variable, then Fredholm-type operators are constant depend only on small parameter. All these effects, as well effects introduced inhomogeneity, developing constructing solutions original problem, implemented work.