2018
Том 70
№ 5

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

Slyusarchuk V. Yu.

Abstract

Let $E$ be a finite-dimensional Banach space, let $C^0(R; E)$ 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 $$\frac{dx(t)}{dt} + (Kx)(t)Ax(t) = h(t),\;t ∈ R.$$

English version (Springer): Ukrainian Mathematical Journal 62 (2010), no. 6, pp 970-981.

Citation Example: Slyusarchuk V. Yu. Conditions for the existence of bounded solutions of nonlinear differential and functional differential equations // Ukr. Mat. Zh. - 2010. - 62, № 6. - pp. 837–846.

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