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In this paper, a class of fourth-order nonlinear neutral dynamic equations on time scales is investigated. We obtain some sufficient conditions for the existence of nonoscillatory solutions tending to zero with some characteristics of the equations by Krasnoselskii's fixed point theorem. Finally, two interesting examples are presented to show the significance of the results. [ABSTRACT FROM AUTHOR]

We study the existence of nonoscillatory solutions tending to zero of a class of third-order nonlinear neutral dynamic equations on time scales by employing Krasnoselskii's fixed point theorem. Two examples are given to illustrate the significance of the conclusions. [ABSTRACT FROM AUTHOR]

In order to improve the performance of the conventional distance protection scheme under high-resistance fault, an adaptive distance protection scheme is proposed in this paper. First, according to the geometric distribution characteristics of voltage and current in the system, the equation of voltage drop from the relaying point to the fault point is established. Second, the fault point is determined by the measured current and the measured negative-sequence current. And then, the new adaptive distance protection criterion is formed according to the relationship between the fault point and the protection zone. Simulation tests on the Real Time Digital Simulator verify that the proposed scheme is able to modify the protection setting value adaptively online, and is immune to the impact of transition resistance and load current. Besides, it has the potential to be applied in a real power system because of small computation amount and high accuracy. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the oscillation of solutions to a class of third-order nonlinear neutral dynamic equations on time scales. New oscillation criteria are presented by employing the Riccati transformation and integral averaging technique. Two examples are shown to illustrate the conclusions. [ABSTRACT FROM AUTHOR]

By means of Schauder fixed point theorem and Banach contraction principle, we investigate the existence and uniqueness of Lipschitz solutions of the equation ρ(f) o f = F. Moreover, we get that the solution f depends continuously on F. As a corollary, we investigate the existence and uniqueness of Lipschitz solutions of the series-like iterative equation ∑n=1∞ anfn(x) = F(x), x ∈ 픹 with a general boundary restriction, where F : 픹 → 픸 is a given Lipschitz function, and 픹, 픸 are compact convex subsets of ℝN with nonempty interior. [ABSTRACT FROM AUTHOR]

We investigate the existence of different types of nonoscillatory solutions to a class of higher-order nonlinear neutral dynamic equations on a time scale. Two examples are provided to show the significance of the conclusions. [ABSTRACT FROM AUTHOR]

For a class of nonlinear higher-order neutral dynamic equations on a time scale, we analyze the existence and asymptotic behavior of nonoscillatory solutions on the basis of hypotheses that allow applications to equations with different integral convergence and divergence of the reciprocal of the coefficients. Two examples are presented to demonstrate the efficiency of new results. [ABSTRACT FROM AUTHOR]