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where and are the minimal and maximal solutions of systems (3.4) and (3.5), respectively, (3.4).

Moreover,, are minimal and maximal solutions of NBVP (2.2) in, respectively.

Here ρ, r are the coupled minimal and maximal solutions of type I for (1.1).

where and are the minimal and maximal solutions of (2.5), (2.6), respectively.

It remains to show that (rho,r) are coupled minimal and maximal solutions of problem (1).

By Theorem 3.2, we know that there exist, which are minimal and maximal solutions of NBVP (2.2) with.

Finally, we prove that is a weakly maximal solution of.

Suppose that is not a weakly maximal solution of.

where r ( t ) is the maximal solution of (3.5).

A feasible solution is called a weakly maximal solution of if.

It follows from Theorem 4.5 that is a weakly maximal solution of.