Affordable Access

On oscillation, continuation, and asymptotic expansions of solutions of linear differential equations

Authors
Publication Date
Disciplines
  • Law
  • Mathematics

Abstract

On oscillation, continuation, and asymptotic expansions of solutions of linear differential equations RENDICONTI del SEMINARIO MATEMATICO della UNIVERSITÀ DI PADOVA STEVENB. BANK On oscillation, continuation, and asymptotic expansions of solutions of linear differential equations Rendiconti del Seminario Matematico della Università di Padova, tome 85 (1991), p. 1-25. <http://www.numdam.org/item?id=RSMUP_1991__85__1_0> © Rendiconti del Seminario Matematico della Università di Padova, 1991, tous droits réservés. L’accès aux archives de la revue « Rendiconti del Seminario Matematico della Università di Padova » (http://rendiconti.math.unipd.it/) implique l’ac- cord avec les conditions générales d’utilisation (http://www.numdam.org/legal. php). Toute utilisation commerciale ou impression systématique est consti- tutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ On Oscillation, Continuation, and Asymptotic Expansions of Solutions of Linear Differential Equations. STEVEN B. BANK (*) 1. Introduction. There is a classical result due mainly to E. Hille (see [13; p. 345] or [22; p. 282]) which states that for any second-order linear differential equation where P(z) and Q(z) are polynomials, there exist finitely many rays, arg z = p,, for j = 1, ..., m, (which can be explicitely calculated from the equation), with the property that for any E &#x3E; 0, all but finitely many ze- ros of any solution f # 0 must lie in the union of the sectors I arg z - - 1Jj E for j = 1, ... , m. In [1], [6], and [7], an investigation was carried out to determine the corresponding situation for higher-order equations, It was first shown in [6] that when the coefficients Rj (z) are polynomi- als, the situation for n &#x3E; 2 can be far different than that for n = 2, since equations of order n &#x3E; 2 c

There are no comments yet on this publication. Be the first to share your thoughts.