Note on bounded L^p-solutions of a generalized Liénard equation

Allan J. Kroopnick

Vol. 94 (1981), No. 1, 171–175

DOI: 10.2140/pjm.1981.94.171

Abstract

Two theorems are presented giving sufficient conditions for all solutions to y′′ + c(t)f(y)y′ + a(t)b(y) = 0 to be bounded. Furthermore, two other theorems are given guaranteeing when these solutions are L^p-solutions. Asymptotic stability is then discussed as well as several applications of these results.

Mathematical Subject Classification 2000

Primary: 34D05

Milestones

Received: 10 April 1978

Revised: 10 August 1980

Published: 1 May 1981