Sentence examples for many dynamic equations from inspiring English sources

There are many dynamic equations available.

Many dynamic equations are available, but their accuracy has been debated.

Due to their importance in numerous application, for example, physics, population dynamics, industrial robotics, optimal control, and other areas, many authors are studying dynamic equations with impulse effects; see [1 - 19] and references therein.

There are more time scales than just (corresponding to the continuous case) and (corresponding to the discrete case) and hence many more classes of dynamic equations.

Since then many authors have investigated the dynamic equations, the calculus of variations and the optimal control problem on time scales (see [2 11]).

Mi and Mu [12] established many dynamic results for a modified Novikov equation with peak solution.

Mi and Mu [11] obtained many dynamic results for a modified Novikov equation with a peak solution.

Differential-algebraic equations (DAE) systems arise naturally from modelling many dynamic systems and are more difficult to handle than ordinary differential equation (ODE) systems.

The authors obtained some new oscillation criteria and extended many known results for oscillation of third-order dynamic equations.

In recent years, there has been an increasing interest in studying oscillatory behavior of second-order neutral delay dynamic equations on time scales, and many results have been obtained; see, for example, [3 7].

Under various growth restrictions on nonlinear term of dynamic equation, many authors have obtained many excellent results for the above problem by using Topological degree theory, fixed-point theorems on cone, bifurcation theory, and so on.