Sentence examples for upper solution for from inspiring English sources

By this, an upper solution for (1.1) is obtained.

We now construct an upper solution for this problem.

An upper solution for (1.1) satisfies the reversed inequalities.

A function is an upper solution for (3.2) if and (3.4).

So, α and β are, respectively, a lower and an upper solution for problem (20).

Similarly, a real-valued function on is an upper solution for (1.1 - 1.2 1.1 - 1.2.

We define lower and upper solutions for problem (3.1).

In Section 2 we develop a method to construct lower and upper solutions for (1.1).

Assume that ((alpha_{1},alpha_{2})), ((beta_{1},betare2})) are coupled lower and upper solutions for the system (1 - 2).

It is elementary matter to check that and,, are lower and upper solutions for the problem.

In this paper, we extended the concept of lower and upper solutions for (1.1).