Abstract
The article investigates a new type of boundary value problems with boundary conditions for only one component of the solution of a system of ordinary differential equations that cannot be investigated for the existence and uniqueness of a solution by traditional methods. In this work, to study this type of non-standard problems with boundary conditions, the method of linear mappings was used. The use of this method for this kind of non-standard problems is justified in the monograph of one of the authors of this article. Three theorems are proved: two on the existence of a solution and one on the uniqueness of a solution. The proof of these theorems follows from M.A. Krasnoselsky’s principle. since the right-hand sides of the system consist of the sum of two operators, the first of them is a contraction operator, and the second is a completely continuous operator.
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