Vol. 75, No. 1, 1978

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Conjugate points for nonlinear differential equations

Kurt Kreith and Charles Andrew Swanson

Vol. 75 (1978), No. 1, 171–184
Abstract

Much of the classical Sturm oscillation theory has a natural generalization to linear selfadjoint differential equations of order 2n if the notion of successive zeros is replaced by that of n n conjugate points. Specifically, the smallest β > α such that

y(α) = y′(α) = ⋅⋅⋅ = y(n−1)(α) = 0 = y(β) = ⋅⋅⋅ = y(n−1)(β)

is satisfied by a nontrivial solution of the equation is called the first conjugate point of α and denoted by η1(α).

Mathematical Subject Classification 2000
Primary: 34C10
Milestones
Received: 9 June 1976
Published: 1 March 1978
Authors
Kurt Kreith
Charles Andrew Swanson