In the paper, we study the oscillation of fourth-order delay differential equations, the present authors used a Riccati transformation and the comparison technique for the fourth order delay differential equation, and that was compared with the oscillation of the certain second order differential equation. Our results extend and improve many well-known results for oscillation of solutions to a class of fourth-order delay differential equations. Some examples are also presented to test the strength and applicability of the results obtained.

Abstract. We establish sufficient conditions for the oscillation of all solutions to the retarded difference equationand the (dual) advanced difference equationwhere (p i (n)), 1 ≤ i ≤ m are sequences of nonnegative real numbers, (τ i (n)), 1 ≤ i ≤ m are sequences of integers such thatΔ denotes the forward difference operator Δx(n) = x(n + 1) − x(n) and ∇ denotes the backward difference operator ∇x(n) = x(n) − x(n − 1). Examples illustrating the results are also given.Mathematics Subject Classification (2010). 39A10, 39A21.

In this paper, stochastic analysis of a diseased prey–predator system involving adaptive back-stepping control is studied. The system was investigated for its dynamical behaviours, such as boundedness and local stability analysis. The global stability of the system was derived using the Lyapunov function. The uniform persistence condition for the system is obtained. The proposed system was studied with adaptive back-stepping control, and it is proved that the system stabilizes to its steady state in nonlinear feedback control. The value of the system is described mostly by the environmental stochasticity in the form of Gaussian white noise. We also established some conditions for oscillations of all positive solutions of the delayed system. Numerical simulations are illustrated, and sustained our analytical findings. We concluded that controlled harvesting on the susceptible and infected prey is able to control prey infection.

No abstract

NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer All rights reserved. This work may not be translated or copied in whole or in part without the written are not identified as such, is not to be taken as an expression of opinion as to whether or not they are The use in this publication of trade names, trademarks, service marks, and similar terms, even if they permission of the

New sets of orthogonal functions, which correspond to the first, second, third, and fourth kind Chebyshev polynomials with half-integer indexes, have been recently introduced. In this article, links of these new sets of irrational functions to the third and fourth kind Chebyshev polynomials are highlighted and their connections with the classical Chebyshev polynomials are shown.

No abstract

No abstract