English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Under certain circumstances differential equations which are analytic functions of a parameter and of the dependent variables admit of periodic solutions which are expansible as converging power series in the parameter. The proof of the existence of the periodic solutions is usually much more laborious than the actual construction of their first terms. Heretofore it has been necessary to give the proof of their existence in each specific case before the validity of the construction was assured. In this paper the problem of proving the existence of the periodic solutions in a very general class of cases will be developed in such a manner that it is closely related to that of their practical construction; and it will be shown from these relations that, whatever the multiplicity of the solutions, when the formal construction is possible the existence proof can be made. Therefore in this class of cases the direct existence proof is no longer necessary, and the complete discussion is correspondingly simplified and shortened.

An existence theorem for periodic solutions