Opuscula Math. 26, no. 3 (2006), 395-406

Opuscula Mathematica

Initial data generating bounded solutions of linear discrete equations

Jaromír Baštinec
Josef Diblík
Miroslava Růžičková

Abstract. A lot of papers are devoted to the investigation of the problem of prescribed behavior of solutions of discrete equations and in numerous results sufficient conditions for existence of at least one solution of discrete equations having prescribed asymptotic behavior are indicated. Not so much attention has been paid to the problem of determining corresponding initial data generating such solutions. We fill this gap for the case of linear equations in this paper. The initial data mentioned are constructed with use of two convergent monotone sequences. An illustrative example is considered, too.

Keywords: linear discrete equation, bounded solutions, initial data.

Mathematics Subject Classification: 39A10, 39A11.

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  • Jaromír Baštinec
  • Brno University of Technology, Department of Mathematics, Faculty of Electrical Engineering and Communication, Technická 8, 616 00 Brno, the Czech Republic
  • Josef Diblík
  • Brno University of Technology, Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Veveří 331/95, 602 00 Brno, the Czech Republic
  • Miroslava Růžičková
  • Žilina University, Department of Applied Mathematics, Faculty of Science, Hurbanova 15, 010 26 Žilina, the Slovak Republic
  • Received: 2005-10-03.
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Cite this article as:
Jaromír Baštinec, Josef Diblík, Miroslava Růžičková, Initial data generating bounded solutions of linear discrete equations, Opuscula Math. 26, no. 3 (2006), 395-406

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