Sentence examples for cases of equation from inspiring English sources

are special cases of equation (2), which of course all have trivial solutions.

In Section 2.1, a classification of limit cases of Equation (1.1) is introduced.

Finally, we give numerical examples of some special cases of Equation (1) and draw it by using Matlab.

Moreover, there are numerous recent results concerning the Hyers-Ulam stability of some particular cases of equation (1).

The Dirichlet problem to some particular cases of equation (1) are considered in [7] (the cases when (alpha=1mbox{ and }1/2)) and in [8].

In Sect. 4 we give the solutions of some special cases of Equation 1 and give a numerical examples of each case and draw it by using Matlab 6.5.

Motivated by the study of the McKean-Vlasov equations, these authors studied special cases of equations (Equation 21).

It is then possible to check all cases of Equations (2) and (3), using again A1.

In this section some particular cases of equations (11) to (13) where the equations are reduced to ordinary differential equations are considered.

The boundary cases of equations and systems have motivated us to study them for the case of non-positive initial values.

For X = R m, such equations are special cases of equations introduced in 1957 by Kurzweil (see [3]) in connection with the advanced study of continuous dependence properties of ordinary differential equations (see also [1]).