Nonlinear Neutral Dynamic Equations Research Articles

The existence and uniqueness of periodic solutions for nonlinear neutral dynamic equation with infinite delay on a Time Scale.

Let   be a periodic time scale. We study the following nonlinear neutral dynamic equation with infinite delay by using a fixed point theorem due to Krasnoselskii, we show that the nonlinear neutral dynamic equation with an infinite delay has a periodic solution. In addition, through utilizing the contraction mapping principle, we have shown that this periodic solution is unique.

Oscillation of Solutions to Third-Order Nonlinear Neutral Dynamic Equations on Time Scales

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.

Oscillation of nonlinear neutral dynamic equations on time scales

The authors present necessary and sufficient conditions for the oscillation of a class of second order non-linear neutral dynamic equations with non-positive neutral coefficients by using Krasnosel’skii’s fixed point theorem on time scales. The nonlinear function may be strongly sublinear or strongly superlinear.

The Existence and Uniqueness of Periodic Solutions for Nonlinear Neutral dynamic equation with infinite delay on a Time Scale

This paper aims to prove the existence and uniqueness of a nonlinear neutral dynamic equation with infinite delay using the Krasnoselskii fixed point method and the contraction mapping principle, respectively.

New oscillation results for non-canonical higher order nonlinear neutral dynamic equations

New oscillation results for non-canonical higher order nonlinear neutral dynamic equations

Existence of nonoscillatory solutions tending to zero of fourth-order nonlinear neutral dynamic equations on time scales

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.

Oscillation Criteria for Third-Order Nonlinear Neutral Dynamic Equations with Mixed Deviating Arguments on Time Scales

Under a couple of canonical and mixed canonical-noncanonical conditions, we investigate the oscillation and asymptotic behavior of solutions to a class of third-order nonlinear neutral dynamic equations with mixed deviating arguments on time scales. By means of the double Riccati transformation and the inequality technique, new oscillation criteria are established, which improve and generalize related results in the literature. Several examples are given to illustrate the main results.

Existence of positive solutions for second-order nonlinear neutral dynamic equations on time scales

AbstractIn this article we study the existence of positive solutions for second-order nonlinear neutral dynamic equations on time scales. The main tool employed here is Schauder’s fixed point theorem. The results obtained here extend the work of Culakova, Hanustiakova and Olach [12]. Two examples are also given to illustrate this work.

Existence of nonoscillatory solutions to nonlinear higher-order neutral dynamic equations

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.

Existence, Uniqueness and Stability of Periodic Solutions for Nonlinear Neutral Dynamic Equations

Existence, Uniqueness and Stability of Periodic Solutions for Nonlinear Neutral Dynamic Equations

Existence of nonoscillatory solutions tending to zero of third-order neutral dynamic equations on time scales

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.

Nonoscillatory solutions to fourth-order neutral dynamic equations on time scales

In this paper, we present some sufficient conditions and necessary conditions for the existence of nonoscillatory solutions to a class of fourth-order nonlinear neutral dynamic equations on time scales by employing Banach spaces and Krasnoselskii’s fixed point theorem. Two examples are given to illustrate the applications of the results.

Oscillation of second-order nonlinear neutral dynamic equations with “Maxima” on time scales

This paper is concerned with the oscillation of solutions of the second order nonlinear neutral delay dynamic equation with “Maxima” of the formon a time scale 𝕋. The obtained results improve and generalize some recent published results. Examples are given to illustrate the main results.

Uncountably many nonoscillatory bounded solutions to second-order nonlinear neutral dynamic equations

This work is devoted to the study of the existence of uncountably many nonoscillatory bounded solutions to second-order nonlinear neutral dynamic equations by means of the Darbo fixed point theorem. We construct assumptions without sign conditions on the nonlinear part of the equation. Moreover, we prove the necessary condition for the existence of an asymptotically zero solution to the problem under consideration.

Study of global asymptotic stability in nonlinear neutral dynamic equations with variable delays

Study of global asymptotic stability in nonlinear neutral dynamic equations with variable delays

Oscillation for a nonlinear neutral dynamic equations on time‐scales with variable exponents

In the present manuscript, we study the oscillation theory for a first‐order nonlinear neutral dynamic equations on timescales with variable exponents of the form urn:x-wiley:mma:media:mma5636:mma5636-math-0001 where ξ is a quotient of odd positive integers; be a fixed number; is a timescale interval; η,τm > 0; for m = 1,2,…,n such that , and the variable exponents αm(t) satisfy . The principal goal of this paper is to establish some new succinct sufficient conditions for oscillation. Furthermore, we introduce a forcing term and then study the oscillation. Afterward, some interesting special cases are also studied to obtain similar sufficient conditions of oscillation under certain conditions. Moreover, the oscillatory behaviour of the solutions of a first‐order neutral dynamic equation on timescale with a nonlocal condition and a forced nonlinear neutral dynamic equation on time scale are studied. But the proofs are based on the prior estimates obtained in this paper. Some enthralling examples are constructed to show the effectiveness of our analytic results. These counterparts are quite different in the literature even when . Finally, the Kamenev‐type and Philos‐type oscillation criterions are established.

Oscillatory behavior of higher order nonlinear homogeneous neutral delay dynamic equations with positive and negative coefficients

Abstract In this paper, we derive some sufficient conditions for the oscillatory and asymptotic behavior of solutions of the higher order nonlinear neutral delay dynamic equation with positive and negative coefficients. The results of this paper extend and generalize the results of [S. Panigrahi and P. Rami Reddy, Oscillatory and asymptotic behavior of fourth order non-linear neutral delay dynamic equations, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 20 2013, 143–163] and [S. Panigrahi, J. R. Graef and P. Rami Reddy, Oscillation results for fourth order nonlinear neutral dynamic equations, Commun. Math. Anal. 15 2013, 11–28]. Examples are included to illustrate the validation of the results.

Study of global asymptotic stability in nonlinear neutral dynamic equations on time scales

This paper is mainly concerned the global asymptotic stability of the zero solution of a class of nonlinear neutral dynamic equations in C1rd. By converting the nonlinear neutral dynamic equation into an equivalent integral equation, our main results are obtained via the Banach contraction mapping principle. The results obtained here extend the work of Yazgan, Tunc and Atan [17].

Existence of positive periodic solutions for nonlinear neutral dynamic equations with variable coefficients on a time scale

Let T be a periodic time scale. The purpose of this paper is to use Krasnoselskii's fixed point theorem to prove the existence of positive periodic solutions for nonlinear neutral dynamic equations with variable coefficients on a time scale. We invert these equations to construct a sum of a contraction and a compact map which is suitable for applying the Krasnoselskii's theorem. The results obtained here extend the work of Candan <cite>c1</cite>.

Global asymptotic stability in nonlinear neutral dynamic equations on time scales

Global asymptotic stability in nonlinear neutral dynamic equations on time scales