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.
- 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.
