Sentence examples for continuous solutions from inspiring English sources

In this region the continuous solutions of the Cosserat equations cannot easily match the continuized fields that by construction are piecewise constant over control volumes of finite size.

Lemma 5.2 (Extension property for continuous solutions).

The existence of such a sequence of Lipschitz continuous solutions of (CP) and the comparison principle for Lipschitz continuous solutions of (CP) guarantees the Theorem 2 holds.

Having shed some light on continuous solutions of the basic difference equation (60), let us now look at restrictions of the continuous solutions to special intervals.

The problem of finding all continuous solutions of equation (2.8) seems to be very difficult.

So far, we have considered the situation of piecewise continuous solutions to (60).

For the case of (a=0) and (bneq0), (4) has no real continuous solutions.

Let moreover be the continuous solutions to the recurrence relation (2.60).

However, all continuous solutions of (1.2) for n ≥ 3 have long been in suspense.

Furthermore, the paper obtained the continuous solutions of (1.3) for the nonhyperbolic case 1 = r 1 < r 2 < ⋯ < r n, and proved no continuous solutions for (1.2) with c ≠ 0 in the case of all characteristic roots being 1.

In [1], it was shown that there exist continuous and piecewise continuous solutions to the difference equation.