Sentence examples for minimal solutions are from inspiring English sources

Some properties concerning the maximal and minimal solutions are also given.

Also, the monotone iterative technique is developed and the existence results for maximal and minimal solutions are obtained.

We establish uniform and optimal gradient estimates of solutions and prove that minimal solutions are non-degenerated.

On the right, weight minimal solutions are shown for m  =  1,..,4.

The results of the minimal solutions are shown in Fig. 5.

By introducing a new type of growth conditions and using the monotone iterative technique, some new results about the existence of maximal and minimal solutions were established, and the estimation of the lower and upper bounds of the maximum and minimum solutions was also derived.

As can be seen in the figure, the number of perturbations that provide minimal solutions is much smaller than the total number of possible perturbations.

A minimal solution is the one that minimizes the summed changes of the 5 variables.

It is obvious that this minimal solution is a global solution, since the particle always travels inertially.

We have proved that the minimal solution is unique; see the Appendix.

In this case, the associated Riccati equation is of the form (24). and its minimal solution is, where is the smaller of (the two real) roots of (2.3).