Existence Of Nonoscillatory Solutions Research Articles

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.

English

english

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 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.

Structure of Non-Oscillatory Solutions for Second Order Dynamic Equations on Time Scales

In this paper, we make a detailed analysis of the structure of non-oscillatory solutions for second order superlinear and sublinear dynamic equations on time scales. The sufficient and necessary conditions for existence of non-oscillatory solutions are presented.

Nonoscillation of higher order mixed differential equations with distributed delays

We are concerned with a class of higher order mixed differential equations with distributed delays. Several new sufficient conditions for the existence of nonoscillatory solutions have been obtained by Schauder–Tychonoff fixed point theorem, which generalize and improve some known results. Two examples are given to explain our main results.

时标上一类二维动力系统的非振荡解的存在性

时标上一类二维动力系统的非振荡解的存在性

On the existence of nonoscillatory solutions of three-dimensional time scale systems

We consider a three-dimensional nonlinear system of first order dynamic equations on time scales and show the existence and asymptotic behavior of nonoscillatory solutions by using the most well-known fixed point theorems. Examples are also provided, which validates our theoretical claims.

Existence of Nonoscillatory Solutions for Fractional Functional Differential Equations

In this paper, we develop sufficient criteria for the existence of a nonoscillatory solution to the fractional neutral functional differential equation of the form: $$\begin{aligned} D^{\alpha }_t[x(t)+c x(t-\tau )]'+\sum ^m_{i=1}P_i(t)F_i(x(t-\sigma _i))=0,\quad t\ge t_0, \end{aligned}$$ where \(D_t^{\alpha }\) is Liouville fractional derivatives of order \(\alpha \ge 0\) on the half-axis, \(c\in \mathbb {R}\), \(\tau \), \(\sigma _i\in \mathbb {R}^+\), \(P_i\in C([t_0, \infty ), \mathbb {R})\), \(F_i\in C(\mathbb {R}, \mathbb {R}), ~ i=1,2,\ldots ,m\), \(m \ge 1\) is an integer. Our results are new and improve many known results on the integer-order functional differential equations.

Existence of nonoscillatory solutions for system of higher-order neutral differential equations with distributed coefficients and delays

In this paper we consider the existence of nonoscillatory solutions for a system of higher-order neutral differential equations with distributed coefficients and delays. We use the Banach contraction principle to obtain new sufficient conditions for the existence of nonoscillatory solutions.

Existence of non-oscillatory solutions for second-order mixed neutral differential equations with positive and negative terms

In this paper, we discuss the existence of non-oscillatory solutions for the second-order mixed neutral differential equations. By means of Banach contraction mapping principle and inequality techniques, some sufficient conditions for the existence and uniqueness of non-oscillatory solutions are presented, which improve and extend some known results. Several examples are given to illustrate our main results.

Existence of Nonoscillatory Solutions to Higher-Order Nonlinear Neutral Dynamic Equations on Time Scales

In this paper, we establish the existence of nonoscillatory solutions to a class of higher-order nonlinear neutral dynamic equations on time scales by employing Kranoselskii’s fixed point theorem. In addition, two examples are included to illustrate the significance of the results.

Existence of nonoscillatory solutions of higher-order neutral differential equations with positive and negative coefficients

In this paper we consider the existence of nonoscillatory solutions of higher-order neutral differential equations with distributed coefficients and delays. We use the $Banach$ contraction principle to obtain new sufficient condition for the existence of nonoscillatory solutions.

Existence of Nonoscillatory Solutions of Higher Order Nonlinear Neutral Nonhomogeneous Equations with Distributed Deviating Arguments

Existence of Nonoscillatory Solutions of Higher Order Nonlinear Neutral Nonhomogeneous Equations with Distributed Deviating Arguments

On nonoscillatory solutions tending to zero of third-order nonlinear dynamic equations on time scales

By Kranoselskii’s fixed point theorem, we state some sufficient conditions of the existence of nonoscillatory solutions tending to zero as $t\rightarrow\infty$ of a class of third-order nonlinear dynamic equations on time scales. Two examples are presented to show the significance of the results.

Existence of Nonoscillatory Solutions of Higher-Order Neutral Differential Equations with Distributed Coefficients and Delays

We consider the existence of nonoscillatory solutions of higher-order neutral differential equations with distributed coefficients. We use theBanachcontraction principle to obtain new sufficient condition for the existence of nonoscillatory solutions.

Existence of Nonoscillatory Solutions of First Order Nonlinear Neutral Dierence Equations

In this paper, we discuss the existence of nonoscillatory solutions of first order nonlinear neutral difference equations of the form
 We use the Knaster-Tarski xed point theorem to obtain some sucient conditions for the existence of nonoscillatory solutions of above equations. Example are given to illustrate the main results.

Existence of Nonoscillatory Solutions for System of Higher-Order Neutral Differential Equations with Distributed Deviating Arguments

In this paper, we consider the existence of nonoscillatory solutions for system of variable coefficients higher-order neutral differential equations with distributed deviating arguments. We use theBanachcontraction principle to obtain new sufficient conditions for the existence of nonoscillatory solutions.

Existence of Nonoscillatory Solutions of a Class of Nonlinear Dynamic Equations with a Forced Term

In this paper, we consider the following forced higher-order nonlinear neutral dynamic equation                 12 0 ,, m k xt p t x t f t x t x t x t q t t t           ,, ,  ,  on time scales. By using Banach contraction principle, we obtain sufficient conditions for the existence of nonoscillatory solutions for general   pt and which means that we allow oscillatory  qt   pt and . We give some ex amples to illustrate the obtained results.  qt