Sentence examples for continuation theory from inspiring English sources

Our proof is based on Mawhin's continuation theory.

In this paper, we try to fill the gap and establish the existence of periodic solution of (1.1) using Mawhin's continuation theory.

In recent years, Lu et al. [5 7] used Mawhin's continuation theory to do research to the existence of a periodic solution for p-Laplacian neutral Rayleigh equation.

We first transform (1.3) into a system of first-order differential equations, and then by applying Mawhin's continuation theory and some new inequalities, we obtain sufficient conditions for the existence of periodic solutions for (1.3).

(1.4) Inspired by these results in [5, 9 11], in this paper, we consider the existence of a positive periodic solution for (1.1) with singularity by applications of Mawhin's continuation theory.

In Section 2, we first give qualitative properties of the neutral operator A which will be helpful for further studies of differential equations with this neutral operator; in Section 3, by applying Mawhin's continuation theory and some new inequalities, we obtain sufficient conditions for the existence of periodic solutions for (1.4), an example is also given to illustrate our results.

The existence of positive solutions for p-Laplacian equation boundary value problems has been studied by many authors applying various nice methods such as topological degree, the Leray-Schauder continuation theorem, coincidence degree theory and so on (see [2, 4, 5, 8 24]).

The multidimensional scaling method, which has been recently developed, is considered to be a continuation of the theory of quantification.

This study is mainly based on continuation theorem in coincidence degree theory and will also give beneficial results for continuous and discrete cases.

by Mawhin's continuation theorem of coincidence degree theory [3].

The proof of the main result relies on a known continuation theorem of coincidence degree theory.