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- Title
On oscillation of solutions of second-order nonlinear difference equations.
- Authors
Koplatadze, R.; Pinelas, S.
- Abstract
We consider the difference equationwhere $$ 0<\lambda <1,\quad p:N\to {R_{+}},\quad \sigma :N\to N,\quad \sigma (k)\geq k+1\quad \mathrm{for}\quad k\in N $$, and the difference operator is defined as follows: $$ \Delta u(k)=u\left( {k+1} \right)-u(k),\;\;{\Delta^2}=\Delta \circ \Delta $$. Necessary conditions are obtained for the above equation to have a positive solution. In addition, oscillation criteria of new type are obtained
- Subjects
NUMERICAL solutions to nonlinear difference equations; DIFFERENCE operators; NUMERICAL solutions to functional differential equations; MATHEMATICAL proofs; MATHEMATICAL analysis; NUMERICAL analysis; OSCILLATION theory of differential equations
- Publication
Journal of Mathematical Sciences, 2013, Vol 189, Issue 5, p784
- ISSN
1072-3374
- Publication type
Article
- DOI
10.1007/s10958-013-1218-8