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

Keywords

Banach Space Nonlinear Differential Equation Functional Differential Equation Linear Continuous Operator Impulsive System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© 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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