Ukrainian Mathematical Journal

, Volume 62, Issue 6, pp 970–981 | Cite as

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

  • V.Yu. Slyusarchuk
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: EE be a linear continuous mapping, and let hC 0(R, E). We establish conditions for the existence of bounded solutions of the nonlinear equation
$$ \frac{{dx(t)}}{{dt}} + \left( {Kx} \right)(t)Ax(t) = h(t),\quad t \in \mathbb{R} $$


Banach Space Nonlinear Differential Equation Functional Differential Equation Linear Continuous Operator Impulsive System 
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© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  • V.Yu. Slyusarchuk
    • 1
  1. 1.National University of Water Management and Nature Resources UseRivneUkraine

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