Abstract
In this paper distribution of zeros of solutions of functional equations in the space of functions of two variables is studied. A zero of a solution in the space of noncontinuous functions is defined. It is demonstrated that oscillatory properties of functional equations are determined by the spectral radius of a corresponding operator acting in the space of essentially bounded functions. Zones of solution positivity are estimated. Various exact oscillation and non-oscillation tests are proposed. A necessary and sufficient condition of oscillation is obtained.
| Original language | English |
|---|---|
| Pages (from-to) | 656-668 |
| Number of pages | 13 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 308 |
| Issue number | 2 |
| DOIs | |
| State | Published - 15 Aug 2005 |
Keywords
- Difference equations
- Oscillation and nonoscillation
- Zeros of solution
- Zones of positivity
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