descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Apr 1959Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 10, page 300 (issn: 0002-9939,

Authors: Tomlinson Fort;

doi: 10.2307/2033595 , 10.1090/s0002-9939-1959-0108611-4

A Problem in Linear Differential Equations

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Abstract

In the Bulletin of the American Mathematical Society, March 1958, page 61, R. E. Bellman suggests the following for research. "Consider the second order linear differential equation (1) u" + (1 + Xg(x))u = O where X is a real constant and fo7 I g(x) I dx 0 for x _ 0, is the singularity nearest the origin on the negative axis?" We assume that g(x) is real for real x. 1. It is known2 that there are two solutions of (1) which we denote by U3(x) and U4(X) such that when x>oo U3(X) sin x > 0, (2) U3 (X) Cos x 0. U4(X) -COS X >0, U4(X) + sin x >0.

Keywords

ordinary differential equations

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