Conjugate points for nonlinear differential equations

Abstract

Much of the classical Sturm oscillation theory has a natural generalization to linear selfadjoint differential equations of order In if the notion of successive zeros is replaced by that of n -n conjugate points.Specifically, the smallest β > a such that y(a) = y'(a) = = /"-»(«) = 0 = y(β) = • • • = y<-"(/3) is satisfied by a nontrivial solution of the equation is called the first conjugate point of a and denoted by r) x {a).