Geodesic
On the existence of a positive solution to a boundary value problem for a third-order nonlinear functional differential equation with an integral boundary condition at one of the ends of the segment
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 34 (2024) no. 3, pp. 311-320

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The article studies the existence of positive solutions on the segment $[0,1]$ of a two-point boundary value problem for one nonlinear third-order functional differential equation with an integral boundary condition at one of the ends of the segment. Using the Go–Krasnoselsky fixed point theorem and some properties of the Green's function of the corresponding differential operator, sufficient conditions for the existence of at least one positive solution to the problem under consideration are obtained. An example is given to illustrate the results obtained.
Keywords: functional differential equation, boundary value problem, cone, Green's function
Mots-clés : positive solution 
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     title = {On the existence of a positive solution to a boundary value problem for a third-order nonlinear functional differential equation with an integral boundary condition at one of the ends of the segment},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
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     url = {http://geodesic.mathdoc.fr/item/VUU_2024_34_3_a0/}
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G. È. Abduragimov. On the existence of a positive solution to a boundary value problem for a third-order nonlinear functional differential equation with an integral boundary condition at one of the ends of the segment. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 34 (2024) no. 3, pp. 311-320. http://geodesic.mathdoc.fr/item/VUU_2024_34_3_a0/