NON-LINEAR DIFFERENTIAL-EQUATIONS WITH MONOTONE SOLUTIONS

The differential equation dy4dt4−y=0 has as a fundamental set of solutions sin t, cos et, etand e−t. The latter of these is distinguished by the properties of being positive and strictly decreasing to zero as t⟶∞. As such, e−tis the prototype of the “monotone solution” whose existence will be demonstrated for a large class of nonlinear differential equations of even order. © 1979, University of California, Berkeley. All Rights Reserved.