Nonlocal boundary-value problems for one-dimensional parabolic second-order equations with integral conditions on the lateral boundary are considered in the articles by A.I. Kozhanov. Higher-dimensional integro-differential equations of higher order with integral conditions on the lateral boundary were not studied earlier. The existence and uniqueness theorems of regular solutions are prove. The method of regularization and the method of continuation in a parameter are employed to establish solvability. In the present article we study integro-differential equations with integral conditions on the lateral boundary and prove existence theorems for regular solutions.
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