Inverse problem for an ordinary integro-differential equation with degenerate kernel and nonlocal integral conditions

T. K. Yuldashev

Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 3 (2016), pp. 19-33

Résumé

This article considers the questions of one value solvability of the nonlocal inverse problem for restore the resource and boundary regimes for a nonlinear Fredholm second-order ordinary integro-differential equation with degenerate kernel. By denoting the integro-differential equation is reduced to a system of algebraic equations with nonlinear right-hand side. This system is solved by the aid of modified Kramer method. By the aid of the given additional conditions is obtained the system of two equations with respect to first and second unknown quantity. Is derived also the formula for calculation the third unknown quantity. It is proved the one value solvability of this system by the method of successive approximations. Is derived also the formula for calculation the third unknown quantity. It is studied the stability of solution of the integro-differential equation with respect to restore quantities.

Détail

Mots-clés : nonlocal inverse problem
Keywords: integro-differential equation, degenerate kernel, system of algebraic equations, one valued solvability.

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