Interval Oscillation Criteria Research Articles

Interval Oscillation Criteria for Fractional Partial Differential Equations with Damping Term

In this article, we will establish sufficient conditions for the interval oscillation of fractional partial differential equations of the form It is based on the information only on a sequence of subintervals of the time space rather than whole half line. We consider f to be monotonous and non monotonous. By using a generalized Riccati technique, integral averaging method, Philos type kernals and new interval oscillation criteria are established. We also present some examples to illustrate our main results.

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

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

Interval Oscillation Criteria for Forced Second-Order Nonlinear Delay Dynamic Equations with Damping and Oscillatory Potential on Time Scales

We are concerned with the interval oscillation of general type of forced second-order nonlinear dynamic equation with oscillatory potential of the formrtg1xt,xΔtΔ+p(t)g2(x(t),xΔ(t))xΔ(t)+q(t)f(x(τ(t)))=e(t), on a time scaleT. We will use a unified approach on time scales and employ the Riccati technique to establish some oscillation criteria for this type of equations. Our results are more general and extend the oscillation criteria of Erbe et al. (2010). Also our results unify the oscillation of the forced second-order nonlinear delay differential equation and the forced second-order nonlinear delay difference equation. Finally, we give some examples to illustrate our results.

Interval oscillation criteria for nonlinear impulsive differential equations with variable delay

Interval oscillation criteria for nonlinear impulsive differential equations with variable delay

Interval Oscillation Criteria for Second-Order Damped Differential Equations with Mixed Nonlinearities

In this paper, we consider the interval oscillation criteria for second-order damped differential equations with mixed nonlinearities $$\begin{aligned} \left( r(t)(x'(t))^\gamma \right) '+p(t)(x'(t))^\gamma +\sum ^n_{i=0}q_i(t)\left| x(g_i(t))\right| ^{\alpha _i}\text {sgn}\ x(g_i(t))=e(t), \end{aligned}$$ where \(\gamma \) is a quotient of odd positive integers, \(\alpha _0=\gamma , \alpha _i>0, i=1,\ 2,\ldots ,n\) with \(r,\ p,\ e\), and \(q_i\in C([t_0,\infty ),\mathbb {R}), r(t)>0, g_i:\ \mathbb {R}\rightarrow \mathbb {R}\) are nondecreasing continuous functions on \(\mathbb {R}\) and \(\lim _{t\rightarrow \infty }g_i(t)=\infty , i=0,\ 1,\ 2,\ldots ,n.\) Our results in this paper extend and improve some known results. Some examples are given here to illustrate our main results.

New interval oscillation criteria for second-order functional differential equations with nonlinear damping

Abstract This paper concerns the oscillation problem of second-order nonlinear damped ODE with functional terms.We give some new interval oscillation criteria which is not only based on constructing a lower solution of a Riccati type equation but also based on constructing an upper solution for corresponding Riccati type equation. We use a recently developed pointwise comparison principle between those lower and upper solutions to obtain our results. Some illustrative examples are also provided to demonstrate our results.

Oscillation of fractional order functional differential equations with nonlinear damping

Abstract In this paper, we are concerned with the oscillatory behavior of a class of fractional differential equations with functional terms. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. Based on a certain variable transformation, by using a generalized Riccati transformation, generalized Philos type kernels, and averaging techniques we establish new interval oscillation criteria. Illustrative examples are also given.

Interval oscillation criteria for functional differential equations of fractional order

In this paper, we are concerned with the oscillatory behavior of a class of fractional differential equations with functional terms. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. By using a variable transformation, a generalized Riccati transformation, Philos type kernels, and the averaging technique, we establish new interval oscillation criteria. Illustrative examples are also given.

Interval oscillation criteria for nonlinear impulsive delay differential equations with damping term

In this paper, a class of second order nonlinear impulsive delay differential equations with damping term is studied. Three factors-impulse, delay and damping that affect the interval qualitative properties of solutions of equations are taken into account together. Several interval oscillation criteria which generalize some known ones, such as, in Huang and Feng (2010), Xing and Zheng (2008) and Liu and Xu (2007), are established. Moreover, examples are also given to illustrate the effectiveness and non-emptiness of our results.

Interval Oscillation Criteria for Second-Order Forced Functional Dynamic Equations on Time Scales

This paper is concerned with oscillation of second-order forced functional dynamic equations of the form(r(t)(xΔ(t))γ)Δ+∑i=0n‍qi(t)|x(δi(t))|αisgn x(δi(t))=e(t)on time scales. By using a generalized Riccati technique and integral averaging techniques, we establish new oscillation criteria which handle some cases not covered by known criteria.

Interval oscillation of a general class of second-order nonlinear impulsive differential equations with nonlinear damping

In this paper, a general class of second-order nonlinear impulsive differential equations with damping is studied. Several interval oscillation criteria which generalize and extend some known ones are established. Moreover, examples are given to illustrate the effectiveness and non-emptiness of our results.

Interval Oscillation Criteria for a Class of Fractional Differential Equations with Damping Term

Some new interval oscillation criteria are established based onthe certain Riccati transformation and inequality techniquefor a class of fractional differential equations with damping term. For illustrating the validity of the established results, we also present some applications for them.

New Oscillation Criteria for Second-Order Forced Quasilinear Functional Differential Equations

We establish some new interval oscillation criteria for a general class of second-order forced quasilinear functional differential equations withϕ-Laplacian operator and mixed nonlinearities. It especially includes the linear, the one-dimensionalp-Laplacian, and the prescribed mean curvature quasilinear differential operators. It continues some recently published results on the oscillations of the second-order functional differential equations including functional arguments of delay, advanced, or delay-advanced types. The nonlinear terms are of superlinear or supersublinear (mixed) types. Consequences and examples are shown to illustrate the novelty and simplicity of our oscillation criteria.

Interval Oscillation Criteria for Second-Order Nonlinear Forced Dynamic Equations with Damping on Time Scales

By using the Riccati transformation technique and constructing a class of Philos-type functions on time scales, we establish some new interval oscillation criteria for the second-order damped nonlinear dynamic equations with forced term of the form(r(t)xΔ(t))Δ+p(t)xΔσ(t)+q(t)(xσ(t))α=F(t,xσ(t))on a time scale𝕋which is unbounded, whereαis a quotient of odd positive integer. Our results in this paper extend and improve some known results. Some examples are given here to illustrate our main results.

New interval oscillation criteria for forced second-order differential equations with nonlinear damping

New interval oscillation criteria for forced second-order differential equations with nonlinear damping

New Interval Oscillation Criteria for Certain Linear Hamiltonian Systems

Using a generalized Riccati transformation and the general integral means technique, some new interval oscillation criteria for the linear matrix Hamiltonian systemU'=(A(t)-λ(t)I)U+B(t)V,V'=C(t)U+(μ(t)I-A*(t))V,t≥t0are obtained. These results generalize and improve the oscillation criteria due to Zheng (2008). An example is given to dwell upon the importance of our results.

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

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

INTERVAL CRITERIA FOR FORCED OSCILLATION OF DIFFERENTIAL EQUATIONS WITH p-LAPLACIAN AND NONLINEARITIES GIVEN BY RIEMANN-STIELTJES INTEGRALS

We consider forced second order differential equation with p -Laplacian and nonlinearities given by a Riemann-Stieltje integrals in the form of ( p ( t ) ϕ ( x ' ( t ) ))' + q 0 ( t ) ϕ ( x ( t )) + ∫ b 0 q ( t; s ) ϕ (s) ( x ( t )) d� ( s ) = e ( t ) ; where ϕ ( u ) := ju j sgn u , ; b 2 (0 ; 1) ; � 2 C (0 ; b ) is strictly increasing such that 0 � (0) 0 on ( t 0; 1), q 2 C ((0 ; 1) (0 ; b )), and � : (0 ; b ) ! R is nondecreasing. Interval oscillation criteria of the El-Sayed type and the Kong type are obtained. These criteria are further extended to equations with deviating arguments. As special cases, our work generalizes, unies, and improves many existing results in the literature.

Interval oscillation criteria for forced Emden-Fowler functional dynamic equations with oscillatory potential

Interval oscillation criteria are established for a second-order functional dynamic equation of Emden-Fowler type with oscillatory potential by applying Riccati and generalized Riccati techniques. The results represent further improvements on those given even for differential and difference equations. Some examples are considered to illustrate the main results.

Interval oscillation criteria for certain forced second-order differential equations

By using generalized Riccati transformations and an inequality due to Hardy et al., several new interval oscillation criteria are established for the nonlinear damped differential equation... The new interval oscillation criteria are different from most known ones in the sense they are based on the information only on a sequence of subintervals of [t0, ∞), rather than on the whole half-line. Our results improve and extend the known some results in the literature.