A Two-Point Boundary Value Problem for a Fourth Order Partial Integro-Differential Equation

Two-point boundary value problem for fourth order partial integro-differential equation is considered. By new unknown function the problem is reduced to an equivalent family of two-point boundary value problems for the Volterra integro-differential equations of second order. By the method of introduction functional parameters are constructed the algorithms for finding of solution to family of two-point boundary value problems for the Volterra integro-differential equations of second order. Conditions of existence unique solution to family of two-point boundary value problems for Volterra integro-differential equations of second order are obtained in the terms of initial data. Criteria of unique solvability to the two-point boundary value problem for fourth order partial integro-differential equation is established.

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