A dynamical criterion for conjugate points

Abstract

This paper presents a technique for establishing the existence of conjugate points for real fourth order differential equations defined on an interval [, 00 ). The point > a is conjugate to a if there exists a nontrivial solution y(x) of the equation which satisfies 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.