Vol. 102, No. 2, 1982

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Picone-type theorems for hyperbolic partial differential equations

Kurt Kreith

Vol. 102 (1982), No. 2, 385–395
Abstract

Sturmian comparison theorems are established for hyperbolic partial differential equations of the form

− (m (t)ut)t + (a(x)ux)x + p(x,t)u = 0

and

− (M (t)vt)t + (A(x)vx)x + P(x,t)v = 0

when these equations are neither assumed to admit a separation of variables, nor to have equal principal parts. As such, the principal results constitute a generalization of the classical Sturm-Picone theorem.

Mathematical Subject Classification 2000
Primary: 35B05
Secondary: 35L10
Milestones
Received: 13 January 1981
Revised: 18 May 1981
Published: 1 October 1982
Authors
Kurt Kreith