Interval Oscillation Criteria Research Articles

Oscillation of Nonlinear Fractional Dynamic Equations with Forcing Term

In this paper, interval oscillation criteria for the nonlinear damped dynamic equations with forcing terms on time scales within conformable fractional derivatives are established. Our approach is determined from the implementation of generalized Riccati transformation, some properties of conformable time-scale fractional calculus, and certain mathematical inequalities. Also, we extend the study of oscillation to conformable fractional Euler-type dynamic equation. Examples are presented to emphasize the validity of the main theorems\enleadertwodots.

Interval oscillation criteria for damped second-order delay differential equations with nonlinearities given by Riemann-Stieltjes integral

The purpose of this paper is to investigate the oscillatory behaviour of certain types of damped second-order forced delay differential equations with nonlinearities given by Riemann-Stieltjes integral. By using the Riccati transformation, some inequalities and integral averaging technique, interval oscillation criteria of both El-Sayed type and Kong type are established. Finally, two examples are presented to illustrate the theoretical results.

Interval oscillation criteria for damped second-order delay differential equations with nonlinearities given by Riemann-Stieltjes integral

The purpose of this paper is to investigate the oscillatory behaviour of certain types of damped second-order forced delay differential equations with nonlinearities given by Riemann-Stieltjes integral. By using the Riccati transformation, some inequalities and integral averaging technique, interval oscillation criteria of both El-Sayed type and Kong type are established. Finally, two examples are presented to illustrate the theoretical results.

Forced oscillation of conformable fractional partial delay differential equations with impulses

In this paper, we establish some interval oscillation criteria for impulsive conformable fractional partial delay differential equations with a forced term. The main results will be obtained by employing Riccati technique. Our results extend and improve some results reported in the literature for the classical differential equations without impulses. An example is provided to illustrate the relevance of the new theorems.

Interval oscillation criteria for linear matrix Hamiltonian systems

The Riccati equation method is used to establish some new oscillatory criteria for Hamiltonian systems in a new direction, which is to break the positive definiteness restriction imposed on one of coefficients of the Hamiltonian system. The obtained results are compared with some well known ones.

Interval oscillation criteria for second order nonlinear forced impulsive differential equations with damping term under variable delay

In this paper, interval oscillation of second order forced impulsive differential equations with damping term under variable delay are studied. We follow the Kong and Philos type class functions and pair of functions (H1, H2) to obtain the oscillation criteria. The results obtained in this paper extend some of the existing results. An example is given to illustrate the main result.

Interval oscillation criteria for impulsive conformable fractional differential equations

In this paper, we derive new interval oscillation criteria for impulsive conformable fractional differential equations having fixed moments of impulse actions. The results are extended to a more general class of nonlinear impulsive conformable fractional differential equations. Examples are also given to illustrate the relevance of the result.

Interval oscillation criteria for second order nonlinear forced impulsive differential equations with damping term under variable delay

In this paper, interval oscillation of second order forced impulsive differential equations with damping term under variable delay are studied. We follow the Kong and Philos type class functions and pair of functions (H1, H2) to obtain the oscillation criteria. The results obtained in this paper extend some of the existing results. An example is given to illustrate the main result.

一类二阶非线性多时滞微分方程的区间振动准则

一类二阶非线性多时滞微分方程的区间振动准则

Interval Oscillation Criteria for Self-adjoint Alpha-Fractional Matrix Differential Systems with Damping

In this paper, we are concerned with the oscillation criteria for self-adjoint alpha-fractional matrix differential system with damping term. By using the generalized Riccati technique and the averaging technique, some new oscillation criteria are obtained.

Interval oscillation criteria for second-order linear differential equations with impulsive effects

This paper discusses how the oscillation of solutions changes by adding an impulsive term to a second-order linear differential equation having only a restoring force term but no damping term. Due to the effect of this impulsive term, the moving speed of a mass point of the equation of motion described by the second-order linear differential equation changes discontinuously. Oscillation theorems are given for this impulsive differential equation. As is well known, when the restoring force term is small, all nontrivial solutions of the equation with no impulsive effects do not oscillate. Even when the restoring force term is small, if the action of the impulsive term compensates, the oscillation criteria obtained are satisfied and all nontrivial solutions oscillate. Several examples are given to confirm this fact and some figures are shown to depict the solution curves of these examples. As shown by the obtained oscillation theorems, there are cases that the impulsive effect promotes the oscillation of solutions, but on the contrary, it may suppress the oscillation of solutions. It is shown by a simulation that there is a case where the impulsive effect suppress the oscillation of solutions. Finally, the obtained results are compared with the previous ones.

The Kamenev type interval oscillation criteria of mixed nonlinear impulsive differential equations under variable delay effects

In this paper, a class of mixed nonlinear impulsive differential equations is studied. When the delay sigma(t) is variable, each given interval is divided into two parts on which the quotients of x(t-sigma(t)) and x(t) are estimated. Then, by introducing binary auxiliary functions and using the Riccati transformation, several Kamenev type interval oscillation criteria are established. The well-known results obtained by Liu and Xu (Appl. Math. Comput. 215:283–291, 2009) for sigma(t)=0 and by Guo et al. (Abstr. Appl. Anal. 2012:351709, 2012) for sigma(t)=sigma_{0} (sigma_{0}geq0) are developed. Moreover, an example illustrating the effectiveness and non-emptiness of our results is also given.

Oscillation for Forced Second-Order Impulsive Nonlinear Dynamic Equations on Time Scales

As the unification and development of impulsive differential equations and difference equations, impulsive dynamic equations on time scales are a powerful tool to simulate the natural and social phenomena. In this paper, we study the interval oscillation of a type of forced second-order nonlinear impulsive dynamic equations with changing signs coefficients. By using the Riccati transformation technique, we obtain some new interval oscillation criteria, based only on information of a sequence of subintervals of positive axis. In addition, we provide an example to illustrate the use of our oscillatory results.

Interval oscillation criteria for second-order nonlinear delay differential equations with damping

Interval oscillation criteria for second-order nonlinear delay differential equations with damping

Interval oscillation criteria for impulsive conformable partial differential equations

In this paper, we present some sufficient conditions for the oscillation of all solutions of forced impulsive delay conformable partial differential equations. We consider two factors, namely impulse and delay that jointly affect the interval qualitative properties of the solutions of those equations. The results obtained in this paper extend and generalize some of the known results for forced impulsive conformable partial differential equations. An example illustrating the results is also given.

Interval oscillation criteria for nonlinear differential equations with impulses and variable delay

In this paper, the interval qualitative properties of a class of second order nonlinear differential equations are studied. For the hypothesis of delay τ(t) being variable, the definitions of “strong zero point” and “weak zero point” are introduced and their effects on the estimation of function x(t−τ(t))∕x(t) on each considered interval are investigated, then Riccati transformation and ω functions are applied to obtain interval oscillation criteria. The known results gained by Huang and Feng (2010) for τ(t) being constant and by Zhou and Wang (2016) for τ(t) being variable are developed.

Interval oscillation criteria for forced mixed nonlinear impulsive differential equations with variable delay

In this paper, the interval qualitative properties of a class of mixed nonlinear impulsive differential equations are studied. Under the hypothesis of delay σ(t) being variable, the ratio of functions x(t−σ(t)) and x(t) on each considered interval is estimated, then Riccati transformation and \omega functions are applied to obtain interval oscillation criteria. The results gained by Özbekler and Zafer (2011) for delay σ(t)=0 and by Guo et al. (2012) for delay σ(t) being nonnegative constant are developed.

Interval oscillation criteria for second-order nonlinear forced differential equations involving variable exponent

In this paper, we establish some interval oscillation criteria for a class of second-order nonlinear forced differential equations with variable exponent growth conditions. Our results not only give the sufficient conditions for the oscillation of equations with variable exponent growth conditions, but also they extend some existing results in the literature for equations with a Riemann-Stieltjes integral. Two examples are also considered to illustrate the main results.

The Kamenev type oscillation criteria of nonlinear differential equations under impulse effects

In this paper, a general class of second-order nonlinear damped differential equations under impulse effects is studied. By introducing an auxiliary function of two variables and using Riccati transformation, several Kamenev type interval oscillation criteria are established, which generalize and extend some known ones, such as those of Huang and Feng. Moreover, examples are given to illustrate the effectiveness and non-emptiness of our results.

Interval oscillation criteria for second-order forced impulsive delay differential equations with damping term

In this paper, we present some sufficient conditions for the oscillation of all solutions of a second order forced impulsive delay differential equation with damping term. Three factors-impulse, delay and damping that affect the interval qualitative properties of solutions of equations are taken into account together. The results obtained in this paper extend and generalize some of the the known results for forced impulsive differential equations. An example is provided to illustrate the main result.