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Conditions of Solvability for Nonlinear Differential Equations with Perturbations of the Solutions in the Space of Functions Bounded on the Axis

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Ukrainian Mathematical Journal Aims and scope

We present the conditions of existence and uniqueness of bounded solutions for a nonlinear scalar differential equation \( \frac{dx(t)}{dt}=f\left(x(t)+h(t)\right) \), t ∈ ℝ, in the case where a function f is continuous on ℝ and a function h is bounded and continuous. In addition, we study the case of an almost periodic function h.

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Authors and Affiliations

  1. National University of Water Management and Utilization of Natural Resources, Rivne, Ukraine

    V. Yu. Slyusarchuk

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, No. 9, pp. 1286–1296, September, 2016.

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Slyusarchuk, V.Y. Conditions of Solvability for Nonlinear Differential Equations with Perturbations of the Solutions in the Space of Functions Bounded on the Axis. Ukr Math J 68, 1481–1493 (2017). https://doi.org/10.1007/s11253-017-1308-8

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  • DOI: https://doi.org/10.1007/s11253-017-1308-8

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