Zur Frage des Maximalbetrages der Lösungen linearer Differentialgleichungen zweiter Ordnung mit Polynomkoeffizienten

Pöschl, Klaus

doi:10.1007/bf01343129

Search citation statements

Order By: Relevance

Paper Sections

Select...

Statement Of the Main Results1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

1954

1988

Publication Types

Select...

Article7

Relationship

Self Cite0

Independent7

Authors

Journals

Cited by 10 publications

(2 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Regarding cases (iii) and (iv) of Theorem 1, we mention the work of Pöschl [20] and Wittich (see [24, pp. 69-70]).…”

Section: Statement Of the Main Resultsmentioning

confidence: 99%

Finite order solutions of second order linear differential equations

Gundersen¹

1988

Trans. Amer. Math. Soc.

152

View full text Add to dashboard Cite

ABSTRACT. We consider the differential equation /" + A(z)f + B(z)f = 0 where A(z) and B(z) are entire functions.We will find conditions on A(z) and B(z) which will guarantee that every solution / ^ 0 of the equation will have infinite order. We will also find conditions on A(z) and B(z) which will guarantee that any finite order solution / ^ 0 of the equation will not have zero as a Borel exceptional value. We will also show that if A(z) and 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.

show abstract

“…Regarding cases (iii) and (iv) of Theorem 1, we mention the work of Pöschl [20] and Wittich (see [24, pp. 69-70]).…”

Section: Statement Of the Main Resultsmentioning

confidence: 99%

Finite order solutions of second order linear differential equations

Gundersen¹

1988

Trans. Amer. Math. Soc.

152

View full text Add to dashboard Cite

show abstract

“…The orders of the transcendental entire solutions of second order linear DE with polynomial coefficients have been investigated in [28], [29], [30]. The results by Frei, Pschl, and Wlttich on the growth of solutions of linear DE are generalized in the third chapter of [6].…”

mentioning

confidence: 99%