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 Plus annual

Presents the access of premium content as premium feature

Premium Content

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 annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this paper, we treat first-order algebraic differential equations whose coefficients belong to a certain type of function field. In the particular case where the coefficients are rational functions, our main result states that for any given sector S in the plane, there exists a positive real number N, depending only on the equation and the angle opening of S, such that any solution y(z), which is meromorphic in S and satisfies the condition z~"y -» co as z -> co in S, must be of the form exp J" czm(\ +o(l)) in subsectors, where c and m are constants. (From this, we easily obtain a similar representation for analytic solutions in S, which are not identically zero, and for which zKy —> 0 as z -» oo in S, where the positive real number K again depends only on the equation and the angle opening of S.)

A representation theorem for large and small analytic solutions of algebraic differential equations in sectors