On the existence of a positive solution to a boundary value problem for one nonlinear functional-differential equation of the second order

Gusen Abduragimov

doi:10.59400/jam.v1i2.200

On the existence of a positive solution to a boundary value problem for one nonlinear functional-differential equation of the second order

Gusen Abduragimov Department of Applied Mathematics, Dagestan State University, 367000 Makhachkala, Russia

Ariticle ID: 200

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DOI: https://doi.org/10.59400/jam.v1i2.200

Keywords: boundary problem, functionally-differential equation, positive solution, cone, green’s function

Abstract

This article considers a boundary value problem for one non-linear second-order functional differential equation on the segment [0, 1] with an integral boundary condition at one of the ends of the segment. Using the well-known Go-Krasnoselsky theorem, sufficient conditions for the existence of at least one positive solution to the problem under consideration are established. A non-trivial example is given, illustrating the fulfillment of the conditions for the unique solvability of the problem posed.

References

[1] Cabada A, Iglesias J. Nonlinear differential equations with perturbed Dirichlet integral boundary conditions. Boundary Value Problems 2021; 2021: 66. doi: 10.1186/s13661-021-01542-5

[2] Benchohra M, Hamani S, Nieto JJ. The method of upper and lower solution for second order differential inclusions with integral boundary conditions. Rocky Mountain Journal of Mathematics 2010; 40(1): 13–26. doi: 10.1216/RMJ-2010-40-1-13

[3] Ahmad B, Nieto JJ. Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions. Bashir Ahmad 2009; 36: 708576. doi: 10.1155/2009/708576

[4] Belarbi A, Benchohra M, Quahab A. Multiple positive solutions for nonlinear boundary value problems with integral boundary conditions. Archivum Mathematicum 2008; 1(1): 1–7.

[5] Abdelkader AB, Benchohra M. Existence results for nonlinear boundary-value problems with integral boundary conditions. Electronic Journal of Differential Equations 2005; 2005(6): 1–10.

[6] Abduragimov GE. On the existence of a positive solution to a boundary value problem for one non-linear ordinary differential equation of the second order (Russian). Results of Science and Technology. Series “Modern Mathematics and Its Applications. Thematic Reviews” 2021; 199: 3–6. doi: 10.36535/0233-6723-2021-199-3-6

[7] Abduragimov GE. On the existence of a positive solution to a boundary value problem for one non-linear second-order differential equation with integral boundary conditions (Russian). Mathematical Physics and Computer Simulation 2022; 25(4): 4–14. doi: 10.15688/mpcm.jvolsu.2022.4.1

[8] Zhou WX. Existence of multiple positive solutions for singular boundary value problems of nonlinear fractional differential equations. Advances in Difference Equations 2014; 2014: 97. doi: 10.1186/1687-1847-2014-97

Published

2023-07-14

How to Cite

Abduragimov, G. (2023). On the existence of a positive solution to a boundary value problem for one nonlinear functional-differential equation of the second order. Journal of AppliedMath, 1(2), 200. https://doi.org/10.59400/jam.v1i2.200

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