Necessary and sufficient conditions for oscillation of odd order neutral delay parabolic differential equations

Oscillation properties of the solutions of a class of odd order neutral delay parabolic differential equations are investigated via the method of differential inequalities.     

时滞抛物方程解振动的充要条件

In this paper, necessary and sufficient conditions for oscillation of solu-tions of delay parabolic equations are obtained.     

抛物型时滞偏微分方程解振动的充要条件

讨论一类多滞量抛物型时滞偏微分方程解的振动性质，获得了其一切解振动的充要条件及一些充分条件；指出了其与普通抛物型偏微分方程解的质的差异．     

Necessary and sufficient conditions for oscillation of second order linear differential equations

Necessary and sufficient conditions are given for oscillations of second order linear differential equationx″+p(t)x′+q(t)x=0.     

Necessary and sufficient conditions for oscillation of first order nonlinear neutral differential equations

In this paper, we prove that every solution of the first order nonlinear neutral differential equation

     

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.     

Necessary and sufficient conditions for oscillation of Robin boundary problems of neutral functional parabolic equations

Some necessary and sufficient conditions for oscillation of the solutions of Robin boundary problems of neutral parabolic equations with several deviating arguments are obtained.     

Oscillation of solutions for certain impulsive vector parabolic differential equations with delays

In this paper, sufficient conditions are established for H-oscillation of solutions of the following impulsive vector parabolic differential equations with delays

     

A NECESSARY AND SUFFICIENT CONDITION FOR THE OSCILLATION OF HIGHER-ORDER NEUTRAL EQUATIONS WITH SEVERAL DELAYS

Consider the higher-order neutral delay differential equationd~t/dt~n(x(t)+sum from i=1 to lp_ix(t-τ_i)-sum from j=1 to mr_jx(t-ρ_j))+sum from k=1 to Nq_kx(t-u_k)=0,(A)where the coefficients and the delays are nonnegative constants with n≥2 even. Then anecessary and sufficient condition for the oscillation of (A) is that the characteristicequationλ~n+λ~nsum from i=1 to lp_ie~(-λτ_i-λ~n)sum from j=1 to mr_je~(-λρ_j)+sum from k=1 to Nq_ke~(-λρ_k)=0has no real roots.     

非线性抛物型时滞微分方程解振动的充要条件

讨论了一类多滞量非线性抛物型时滞微分方程解的振动性质，获得了其一切解振动的充要条件；指出了其与普通抛物型偏微分方程解的质的差异。     

Necessary and sufficient conditions for the oscillation of solutions of nonlinear differential equations with pulse influence in a banach space

We obtain necessary and sufficient conditions for the oscillation of solutions of nonlinear second-order differential equations with pulse influence in a Banach space. Rovno Technical University, Rovno. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 1, pp. 98–109, January, 1999.     

Stability for impulsive functional differential equations with infinite delays

In this paper, some theorems of uniform stability and uniform asymptotic stability for impulsive functional differential equations with infinite delay are proved by using Lyapunov functionals and Razumikhin techniques. An example is also proved at the end to illustrate the application of the obtained results.     

Boundedness results for impulsive functional differential equations with infinite delays

In this paper, boundedness criteria are established for solutions of a class of impulsive functional differential equations with infinite delays of the form $$\begin{gathered} x'(t) = F(t,x( \cdot )), t > t^ * \hfill \\ \Delta x(t_k ) = I(t_k ,x(t_k^ - )), k = 1,2,... \hfill \\ \end{gathered} $$ By using Lyapunov functions and Razumikhin technique, some new Bazumikhin-type theorems on boundedness are obtained.     

Necessary and sufficient conditions for oscillation of second‐order dynamic equations on time scales

In this paper, we establish necessary and sufficient conditions for oscillation of second‐order strongly superlinear and strongly sublinear dynamic equations. Our results unify and improve many known results in the literature.     

Some sufficient conditions for oscillation of impulsive delay hyperbolic systems with Robin boundary conditions

This paper deals with the oscillation problems of delay hyperbolic systems with impulses. Some sufficient conditions for oscillations of impulsive delay hyperbolic systems with Robin boundary conditions are obtained and the criteria of oscillation of the systems are established.     

Necessary and sufficient conditions for the existence of equilibrium in abstract non-autonomous functional differential equations

In this article, we aim to establish necessary and sufficient conditions that guarantee the existence of equilibria and continuous equilibria for the continuous skew-product semiflow induced by a class of abstract non-autonomous finite-delay functional differential equations without any monotone conditions assumed. A minimal set is constructed in terms of which necessary and sufficient conditions for a continuous equilibrium to exist are also obtained. Several illustrative examples are employed to demonstrate our results.