Determination of the coefficient and boundary regime in boundary value problem for integro-differential equation with degenerate kernel

Abstract

This article examines questions of unique solvability for an inverse boundary value problem to recover the coefficient and boundary regime of a nonlinear integro-differential equation with degenerate kernel. We propose a novel method of degenerate kernel for the case of inverse boundary value problem for the considered ordinary integro-differential equation of second order. By the aid of denotation, the integro-differential equation is reduced to a system of algebraic equations. Solving this system and using additional conditions, we obtained a system of two nonlinear equations with respect to the first two unknown quantities and a formula for determining the third unknown quantity. We proved the single-value solvability of this system using the method of successive approximations.