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Existence of positive solutions to vector boundary value problems I. (English) Zbl 0952.34017
The author deals with a second-order \(n\)-dimensional vector differential system with Dirichlet boundary value conditions. A sufficient condition is given for definition intervals that guarantees the existence of a positive solution to the differential system when some other assumptions of the differential system are fulfilled. The proof of the main result is based on some auxiliary lemmas and on the Brouwer degree of mappings. This paper is the first part of the author’s work on this problem.

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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