Sentence examples for by using topological degree from inspiring English sources

The result is obtained by using topological degree theory.

We also consider the multiplicity of the solutions by using topological degree theory.

By using topological degree theory, some results on the existence of periodic solutions are obtained.

In Section 3, the multiplicity of the solutions is concerned by using topological degree theory.

In this section, we study the multiplicity of the solutions by using topological degree theory.

By using topological degree theory, a new result on the existence of positive periodic solutions is obtained.

The existence and multiplicity of positive solutions for (1.1) with (lambdaequiv1) have been extensively studied by many authors using topological degree theory, fixed point theorems, lower and upper solution methods, and critical point theory (see, for example, [2 17] and the references therein).

Wang et al. [26] investigated the existence theory and proved some conditions for uniqueness and derived some data dependency results of solutions using topological degree technique by considering some classes of non-local Cauchy problems including BVPs and impulsive Cauchy problems (ICPs) to FDEs.

Then using topological degree theory and Leray-Schauder's-type fixed point theorem, existence and uniqueness results are proved.

Now we begin by showing that Lemma 3.2 holds, and use topological degree theory.

If so, how should one use topological degree theory to study the almost periodic systems?