Sturm separation and comparison theorems for a class of fourth order ordinary and partial differential equations

Abstract

Separation and comparison theorems for differential equations of order greater than two appear to be relatively rare. We are concernd here with such theorems for a special class of fourth order ordinary and partial differential equations. For example, a typical comparison theorem is as follows: Suppose 0>c>C, 0(d) c(d) cin R. If there exists a function u>0 in R, u(d) 0 in any open subset of R, satisfying (d)=0 in R, u=(d) =0 on oR, then every solution of the system (d)=0in R, (d) has a zero in R