An oscillation criterion for forced half-linear differential equations with mixed nonlinearities

In this note, a new oscillation criterion for forced half-linear second order differential equations with mixed nonlinearities is obtained by using a generalized Riccati transformation. The result of this note generalizes and improves some previous results in the literature.     

New oscillation criteria for a class of second-order nonlinear forced differential equations

By using classical variational principle and averaging technique, new oscillation criteria are established for second-order nonlinear forced differential equations

     

Interval oscillation criteria for second-order forced impulsive differential equations with mixed nonlinearities

In this paper, by arithmetic-geometric mean inequality and Riccati transformation, interval oscillation criteria are established for second-order forced impulsive differential equation with mixed nonlinearities of the form

     

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

In this paper, we are concerned with the oscillations in a class of forced second-order differential equations with nonlinear damping terms. By using classical variational principle and averaging technique, several new interval oscillation criteria for the equations are established, which improve and extend some known results. Example is also given to illustrate the results.     

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.     

Note on forced oscillation of nth-order sublinear differential equations

In the case of oscillatory potentials, we establish an oscillation theorem for the forced sublinear differential equation x(n)+q(t)λ|x|sgnx=e(t), t∈[t₀,∞). No restriction is imposed on the forcing term e(t) to be the nth derivative of an oscillatory function. In particular, we show that all solutions of the equation x^″+tαsintλ|x|sgnx=mtβcost, t?0, 0<λ<1 are oscillatory for all m≠0 if β>(α+2)/(1−λ). This provides an analogue of a result of Nasr [Proc. Amer. Math. Soc. 126 (1998) 123] for the forced superlinear equation and answers a question raised in an earlier paper [J.S.W. Wong, SIAM J. Math. Anal. 19 (1988) 673].     

Sufficient conditions for the oscillation of forced super-linear second order differential equations with oscillatory potential

In the case of oscillatory potentials, we give sufficient conditions for the oscillation of the forced super-linear equation

This answers a question raised by J. S. W. Wong.

     

On the forced oscillation of solutions for systems of impulsive parabolic differential equations with several delays

In this paper, we study the forced oscillation of certain systems of impulsive parabolic differential equations with several delays. Some oscillation criteria are established.     

On the forced oscillation of systems of neutral parabolic differential equations with deviating arguments

Sufficient conditions are established for the forced oscillation of systems of neutral parabolic differential equations with deviating arguments. The main results are illustrated by some examples.     

On oscillation and asymptotic behaviour of solutions of forced first order neutral differential equations

In this paper, sufficient conditions have been obtained under which every solution of

Kamenev-type oscillation criteria for delay difference equations

Some oscillation criteria are established by Raccati transformation techniques for the following second-order nonlinear neutral difference equation Δ(pn(Δ(xn cnxn-τ))γ) qnxβn-σ=0,n=0,1,2…which extend and include several oscillation criteria in [11], and also correct a theorem and its proof in [10].     

Linearized oscillation theorems for neutral difference equations

Consider the nonlinear neutral difference equation {fx149-1} We establish a linearized oscillation theorem which is a discrete result of the open problem by Gyori and Ladas. This work is partially supported by NNSF (NO: 19671027) of China.     

Nonoscillation criteria for forced second order nonlinear equations

This paper is concerned with nonoscillation criteria and asymptotic behaviour for forced second order nonlinear differential equations. These results improve and include several well-known results.     

Comparison results for oscillation of nonlinear differential equations

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