Sentence examples for using the continuation from inspiring English sources

Then the uniqueness of the solution on [ 0, T ] is direct using the continuation property.

(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.

By using the continuation theorem due to Ge, we obtain some existence results for such boundary value problems.

By using the continuation theorem of Manásevich and Mawhin, a new result on the existence of positive periodic solution is obtained.

Gao et al. [8, 9] considered the existence of periodic solutions for two kinds of Rayleigh type p-Laplacian equations by using the continuation theorem.

A second approach is to use the continuation method.

For our numerical investigations, we used the continuation package Auto[55, 56] for solving the boundary value problems.

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

In this section, we shall use the continuation Lemma 2.1 given in Section 2 to prove Theorem 1.1.

Finally, in order to compute the solution of ((mathcal {P}_{S})), we use the continuation parameter λ 3 to pass from ((mathcal {P}_{R})) to ((mathcal {P}_{S})).