Abduragimov G.E., Abduragimova P.E., Kuramagomedova M.M. On the Existence and Uniqueness of a Positive Solution to a Boundary Value Problem for a Nonlinear Ordinary Differential Fourth Order Equation

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https://doi.org/10.15688/mpcm.jvolsu.2023.3.1

Gusen E. Abduragimov
Candidate of Sciences (Physics and Mathematics), Associate Professor, Department of Applied Mathematics,
Dagestan State University
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https://orcid.org/0000-0003-0542-1149 
Prosp. Lenina, 28, 400005 Volgograd, Russian Federation

Patimat E. Abduragimova
Class Master, Department of Applied Mathematics,
Dagestan State University
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https://orcid.org/0000-0001-9050-0209
Dzerzhinskogo St, 12, 367025 Makhachkala, Russian Federation

Madina M. Kuramagomedova
Candidate for a Degree, Department of Applied Mathematics,
Dagestan State University
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https://orcid.org/0000-0001-6424-9348
Dzerzhinskogo St, 12, 367025 Makhachkala, Russian Federation

Abstract. The article deals with the boundary value problem. This problem is reduced to an equivalent integral equation, the kernel of which is the Green’s function. Using the well-known Go—Krasnoselsky theorem, we prove the existence of at least one positive solution in some cone of the problem under consideration. Further, using a priori estimates, relying on the principle of compressed mappings, the uniqueness of such a solution is established. In conclusion, an example illustrating the results obtained is given.

Key words: boundary value problem, positive solution, Green’s function, cone, differential equations.

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On the Existence and Uniqueness of a Positive Solution to a Boundary Value Problem for a Nonlinear Ordinary Differential Fourth Order Equation by Abduragimov G.E., Abduragimova P.E., Kuramagomedova M.M. is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English: Mathematical Physics and Computer Simulation. Vol. 26 No. 3 2023, pp. 5-11

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