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Existence and Uniqueness of a Positive Solution to a Boundary Value Problem for a Second Order Functional-Differential Equation

Abstract

In the paper, we consider a boundary value problem for a second order functional-differential equation with sufficiently general linear homogeneous boundary conditions. On the basis of the theory of semi-ordered spaces and with the help of special topological methods, we prove the existence of a unique positive solution to the problem.

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Correspondence to G. E. Abduragimov.

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Dedicated to the bright memory of my father, Abduragimov Elderkhan Israpilovich

Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 12, pp. 3–8.

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Abduragimov, G.E. Existence and Uniqueness of a Positive Solution to a Boundary Value Problem for a Second Order Functional-Differential Equation. Russ Math. 65, 1–5 (2021). https://doi.org/10.3103/S1066369X2112001X

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  • DOI: https://doi.org/10.3103/S1066369X2112001X

Keywords

  • positive solution
  • boundary value problem
  • cone
  • asymptotic derivative
  • spectral radius.