Nonlinear differential equations with monotone solutions

Kurt Kreith

Vol. 81 (1979), No. 1, 101–111

DOI: 10.2140/pjm.1979.81.101

Abstract

The differential equation dy⁴∕dt⁴ − y = 0 has as a fundamental set of solutions sint, cost, e^t, and e^−t. The latter of these is distinguished by the properties of being positive and strictly decreasing to zero as t →∞. As such, e^−t is the prototype of the “monotone solution” whose existence will be demonstrated for a large class of nonlinear differential equations of even order.

Mathematical Subject Classification 2000

Primary: 34C10

Milestones

Received: 10 June 1977

Revised: 3 May 1978

Published: 1 March 1979