Finite order solutions of second order linear differential equations
Gary G. Gundersen
Source record
Source: Crossref
Published: Jan 1, 1988
DOI: 10.1090/s0002-9947-1988-0920167-5
Open original source ↗Source abstract
We consider the differential equation f + A ( z ) f ′ + B ( z ) f = 0 f + A(z)f’ + B(z)f = 0 where A ( z ) A(z) and B ( z ) B(z) are entire functions. We will find conditions on A ( z ) A(z) and B ( z ) B(z) which will guarantee that every solution f ≢ 0 f\not \equiv 0 of the equation will have infinite order. We will also find conditions on A ( z ) A(z) and B ( z ) B(z) which will guarantee that any finite order solution f ≢ 0 f\not \equiv 0 of the equation will not have zero as a Borel exceptional value. We will also show that if A ( z ) A(z) and B ( z ) B(z) satisfy certain growth conditions, then any finite order solution of the equation will satisfy certain other growth conditions. Related results are also proven. Several examples are given to complement the theory.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.