On the differential equation y″+exp (y^m−t)=0

Article type: Research Article

Authors: Volkmer, Hans

Affiliations: Department of Mathematical Sciences, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, WI 53201, USA

Abstract: It is shown that the zero T(a) of the solution y(·,a) of y″+exp (ym−t)=0, y(t,a)→a as t→∞, satisfies T(a)=(1−(m/2))am+(m−1)log a+log (m/2)+3/2(m−1)+Ol((log 3a)/(am))  as a→∞ if 1≤m<2. This asymptotic expansion of T(a) is related to a result of Atkinson and Peletier (1986). Moreover, if m=2 then T(a)=log a+s0+O((log 3a)/(am))  as a→∞ where s0=s=1.6853749… is the solution of the transcendental equation s−1.5=exp (−s).

DOI: 10.3233/ASY-1995-10104

Journal: Asymptotic Analysis, vol. 10, no. 1, pp. 63-75, 1995