Vol. 58, No. 1, 1975

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A dynamical criterion for conjugate points

Kurt Kreith

Vol. 58 (1975), No. 1, 123–132
Abstract

This paper presents a technique for establishing the existence of conjugate points for real fourth order differential equations defined on an interval [α,). The point β > α is conjugate to α if there exists a nontrivial solution y(x) of the equation which satisfies

y(α) = y′(α ) = 0 = y(β) = y′(β).

An important feature of this technique is that it is not limited to equations of selfadjoint type and that the general theory applies to nonlinear equations as well.

Mathematical Subject Classification 2000
Primary: 34C10
Milestones
Received: 5 March 1974
Published: 1 May 1975
Authors
Kurt Kreith