On the asymptotic form of the Titchmarsh-Weyl m -coefficient†
- 1 December 1978
- journal article
- research article
- Published by Taylor & Francis in Applicable Analysis
- Vol. 8 (2) , 153-169
- https://doi.org/10.1080/00036817808839223
Abstract
The asymptotic form of the Titchmarsh-Weyl m-coefficient for the differential equation −(py′)′+q j = λwy on [a, b). (′≡d/dx), as |λ|→∞, is obtained under general conditions on the real-valued coefficients p, q and w, with p≧0 and w≧0. Examples are given to show that the result is near to but possible, although there are many interesting cases for which the asymptotic form of the m-coefficient is still not known.Keywords
This publication has 3 references indexed in Scilit:
- On a Class of Integral InequalitiesJournal of the London Mathematical Society, 1978
- On a Property of the M -Coefficient of a Secondorder Linear Differential EquationJournal of the London Mathematical Society, 1972
- ber gew hnliche Differentialgleichungen mit Singularit ten und die zugeh rigen Entwicklungen willk rlicher FunktionenMathematische Annalen, 1910