In this paper discrete inequalities are used to offer sufficient conditions for the oscillation of all solutions of the difference equation Ε½ . n n n q 1 n q 1 n where 0 -s prq with p, q odd integers, or p even and q odd integers. Several examples which dwell upon the importance of our results are
Oscillation of Certain Second Order Nonlinear Difference Equations
β Scribed by B.G. Zhang; G.D. Chen
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 154 KB
- Volume
- 199
- Category
- Article
- ISSN
- 0022-247X
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β¦ Synopsis
In this paper we consider the second order nonlinear difference equation
Γ 4 nondecreasing, and uf u ) 0 as u / 0, q is a real sequence. Some new n Ε½ . sufficient conditions for the oscillation of all solutions of 1 are obtained.
π SIMILAR VOLUMES
1 Ε½ Ε½ .. Ε½ . where ) 0 is any quotient of odd integers, a g C R, 0, Ο± , q g C R, R , Ε½ . Ε½ . Ε½ . fgC R, R , xf x ) 0, f Π x G 0 for x / 0. Some new sufficient conditions for Ε½ . the oscillation of all solutions of ) are obtained. Several examples that dwell upon the importance of our results are als
In this paper, we are mainly concerned with the second order nonlinear difference equation with continuous variable. Here, by using the iterated integral transformations, generalized Riccati transformations, and integrating factors, we give some oscillatory criteria for this equation.
In this paper we are concerned with some new criteria for the oscillation and nonoscillation of the second-order nonhomogeneous linear difference equations of Ε½ . Γ 4Γ 4 Γ 4 the form β¬ c β¬ x q q x s f , n s 1, 2, . . . , where c , f , and q are ny 1 ny1 n n n n n n real sequences, c ) 0 for n G 0, a