Abstract:
In this article we consider a nonlocal problem for a second-order differential equation in the characteristic domain with integral conditions of the first kind. By introducing a new unknown function we reduce the original problem to the equivalent one with nonlocal conditions containing the unit as kernels. Next, we were able to prove the uniqueness of the solution to the problem and perform the transition to the operator equation. At this stage we justify the complete continuity of the obtained operator. From this, and also due to the previously proven uniqueness of the solution, the solvability of the operator equation follows. Since the original problem is equivalent to an operator equation whose solution exists, then the solution to the original problem also exists. As a result of the study, we found the conditions under which exists a solution to original problem. We also formulated and proved the corresponding theorem on the existence and uniqueness of the solution to the problem under consideration.
Keywords:nonlocal integral conditions of the first kind, existence of a solution, completely continuous operator.
