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Conditions for the existence of bounded solutions of nonlinear differential and functional differential equations

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Let E be a finite-dimensional Banach space, let C0(R; E) be a Banach space of functions continuous and bounded on R and taking values in E; let K:C 0(R ,E) → C 0(R, E) be a c-continuous bounded mapping, let A: E → E be a linear continuous mapping, and let h ∈ C 0(R, E). We establish conditions for the existence of bounded solutions of the nonlinear equation

$$ \frac{{dx(t)}}{{dt}} + \left( {Kx} \right)(t)Ax(t) = h(t),\quad t \in \mathbb{R} $$

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Authors and Affiliations

  1. National University of Water Management and Nature Resources Use, Rivne, Ukraine

    V.Yu. Slyusarchuk

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  1. V.Yu. Slyusarchuk
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 6, pp. 837–846, June, 2010.

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Slyusarchuk, V. Conditions for the existence of bounded solutions of nonlinear differential and functional differential equations. Ukr Math J 62, 970–981 (2010). https://doi.org/10.1007/s11253-010-0404-9

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  • DOI: https://doi.org/10.1007/s11253-010-0404-9

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