Sentence examples for auxiliary notion from inspiring English sources

In order to treat the Palais-Smale condition, we need to introduce an auxiliary notion.

Now, in order to prove that the functional I satisfies the Palais-Smale condition, we will introduce an auxiliary notion.

First let us introduce some auxiliary notions.

To shorten the foregoing considerations, we introduce some auxiliary notions as follows.

To investigate the problem (3.1)–(3.5), we need some auxiliary notions given below.

In the following we recall some auxiliary notions and results in a b-metric space [7 9, 11] which are needed subsequently.

To facilitate the presentation of the proof of Theorem 2.3, we introduce an auxiliary tool, namely, the notion of reachable sets.

In this section, to make our exposition self-contained, we recall some basic definitions, relevant notions and auxiliary results.

In this section, to make our exposition self contained, we recall some basic definitions, relevant notions and auxiliary results: Definition 1 [45].

In a Swedish interview study of doctors, nurses and auxiliary nurses on professional identities, notions about femininity and masculinity were expressed without seeing the existing gender order as problematic [ 24].

In Section 2, we introduce an auxiliary nonlinear boundary value problem and the notions of upper and lower solutions used later.