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

  • V. Yu. Slyusarchuk

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 $$\frac{dx(t)}{dt} + (Kx)(t)Ax(t) = h(t),\;t ∈ R.$$
Published
25.06.2010
How to Cite
SlyusarchukV. Y. “Conditions for the Existence of Bounded Solutions of Nonlinear Differential and Functional Differential Equations”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, no. 6, June 2010, pp. 837–846, https://umj.imath.kiev.ua/index.php/umj/article/view/2914.
Section
Research articles