Sentence examples for utilizing the continuation theorem from inspiring English sources

By utilizing the continuation theorem, the comparison theorem, some analysis techniques, and constructing a suitable Lyapunov functional, some sufficient conditions for the existence of positive periodic solutions, permanence, and global attractivity of the system are obtained.

To obtain the existence of positive ω -periodic solutions of system (2), we will use the continuation theorem.

Firstly, recall the continuation theorem of Mawhin.

Our approach is based on the continuation theorem of the coincidence degree, a priori estimates, and differential inequalities.

For the reader's convenience, we will introduce the continuation theorem in the following.

Now, with the above notation, we are ready to state the continuation theorem.

Let us first introduce the continuation theorem due to Gaines and Mawhin [30].

Next, let us recall the continuation theorem in coincidence degree theory.

Based on the continuation theorem of coincidence degree theory, a novel sufficient condition with respect to the existence of periodic solution for CNNs is derived.

(1.2) Using the continuation theorem of coincidence degree theory, they obtained the existence of periodic solutions for (1.2).

By using the continuation theorem and some analysis techniques, some new results on the existence of periodic solutions are obtained.