Geodesic
On the existence of a positive solution to a boundary-value problem for a nonlinear second-order functional differential equation
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 2, Tome 221 (2023), pp. 3-9

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In this paper, we consider a boundary-value problem for a second-order nonlinear functional-differential equation with a strong nonlinearity on the interval $[0,1]$ with integral boundary conditions. Using special topological tools, we obtain sufficient conditions for the existence of a unique positive solution of the problem. The existence of a positive solution is proved by applying the well-known cone dilation theorem, and the uniqueness is established by using the uniqueness principle for convex operators. An example is given, which illustrates the fulfillment of sufficient conditions for the unique solvability of the problem.
Mots-clés : positive solution
Keywords: boundary value problem, cone, cone extension. 
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     title = {On the existence of a positive solution to a boundary-value problem for a nonlinear second-order functional differential equation},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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     publisher = {mathdoc},
     volume = {221},
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     url = {http://geodesic.mathdoc.fr/item/INTO_2023_221_a0/}
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G. È. Abduragimov. On the existence of a positive solution to a boundary-value problem for a nonlinear second-order functional differential equation. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 2, Tome 221 (2023), pp. 3-9. http://geodesic.mathdoc.fr/item/INTO_2023_221_a0/