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

Gusen Abduragimov

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 of 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.


Keywords

boundary problem; functionally-differential equation; positive solution; cone; green’s function

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References

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