Sentence examples for ordered interval of from inspiring English sources

The ordered interval of is written as.

On the other hand it relies on the construction of non-overlapping ordered intervals of sub supersolutions by the use of appropriately designed quasilinear elliptic problems and the maximum and anti-maximum principles.

It is well known that nonlinear problems always have at least one solution in the ordered interval defined by one pair of well-ordered upper and lower solutions.

We know that has in the order interval of least fixed point and greatest fixed point.

Existence and uniqueness of nontrivial solution are presented in an order interval of a cone by using fixed point methods.

If,,, and, then has in an order interval of least and greatest fixed points and they are increasing in.

The proof of the existence of extremal solutions within a given order interval of sub- and supersolutions is the main goal of this paper.

X is Hausdorff and the order intervals of X are closed; if the cone (X^) is normal, then every order interval is bounded.

Then the following assertions hold: (1) X is Hausdorff and the order intervals of X are closed;   (2) if the cone (X^) is normal, then every order interval is bounded.  .

Note that the minimization problems in [1, 3, 7] are taking over order intervals of potentials/weights which are compact in the weak topologies, and therefore always have minimizers.

However, if we modify the Birkhoff interpretation by defining ([a,c,b]_O) to hold just in case (([a,c,b]_Pvee (c=a)vee (c=b))) does (where (vee ) is logical disjunction), then we clearly have an R-relation whose collection of order intervals of the form ([a,b]_O:=[a,b]_Pcup {a,b}) provides an inducing road system.