Sentence examples for upper solutions of from inspiring English sources

Obviously,, are lower and upper solutions of (4.1), respectively, and.

Let and be, respectively, lower and upper solutions of (5.1).

Let be strict upper solutions of (1.1) and for each.

Thus, are lower and upper solutions of (3.14), respectively.

Thus, we have shown that and are lower and upper solutions of BVP (1.1), respectively.

Let and be respective strict -lower and upper solutions of problem (1.1) and (1.2) with on.

We introduce the notion of lower and upper solutions of problem (1.7).

which imply that and are, respectively, lower and upper solutions of (3.7).

are lower and upper solutions of (1.1), respectively, and, for all ;   the function satisfies.

and are, respectively, lower and upper solutions of (1.1) such that.

(B1) and are, respectively, lower and upper solutions of (1.1) such that.