Some Oscillation and Non-Oscillation Theorems for Fourth Order Difference Equations
Copyright policy )Some Oscillation and Non-Oscillation Theorems for Fourth Order Difference Equations
Sufficient conditions are established for oscillation of all solutions of the fourth order difference equation \Delta a_n \Delta (b_n \Delta (c_n \Delta y_n)) + q_n f (y_{n+1}) = h_n \\ (n \in \mathbb N_0) where \Delta is the forward difference operator \Delta y_n = y_{n+1} – y_n, \{a_n\}, \{b_n\}, \{c_n\}, \{q_n\}, \{h_n\} are real sequences, and f is a real-valued continuous function. Also, sufficient conditions are provided which ensure that all non-oscillatory solutions of the equation approach zero as n \to \infty . Examples are inserted to illustrate the results.
- Periyar University India
- University of Madras India
Stability of difference equations, oscillation, fourth order difference equation, non-oscillatory solutions
Stability of difference equations, oscillation, fourth order difference equation, non-oscillatory solutions
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