Sentence examples for many positive solutions from inspiring English sources

Thus (2.29) has at most finitely many positive solutions.

Then we generalized this to obtain many positive solutions.

Consequently Theorem 2.1 implies that Eq. (3.1) possesses uncountably many positive solutions in (A(N,M)).

Equation (1.1) possesses uncountably many positive solutions in (A(N,M)).

Now we shall discuss the existence of infinitely many positive solutions.

4, we discuss the existence of denumerably many positive solutions of system (1.1)–(1.1).

Some ideas of the existence of denumerably many positive solutions are from [45].

Thus Theorem 2.4 shows that Eq. (3.4) possesses uncountably many positive solutions in (A(N,M)).

Therefore, by Theorem 4.2 we know that problem (5.7) has countably many positive solutions such that.

Then problem (1.5) has countably many positive solutions such that for each.

In Section 4, we prove the existence of countably many positive solutions for problem (1.5) under suitable conditions on and.