M(\(\lambda\) ) theory for singular Hamiltonian systems with two singular points. (English) Zbl 0694.34013

The present work is a continuation of an earlier work of the author [ibid. 20, No.3, 664-700 (1989; Zbl 0683.34008)]. In this work, the 2m- dimensional Hamiltonian system \(JY'=(\lambda A+B)Y\) on an interval (a,b) is considered, where both a and b are singular points. A Green’s function is derived using separated singular boundary conditions and it is used to show that the singular boundary value problem consisting of the differential equation and boundary conditions is self-adjoint. A doubly singular version of Green’s formula is derived and all self-adjoint boundary value problems arising from the differential equation are characterized.
Reviewer: N.Parhi


34B05 Linear boundary value problems for ordinary differential equations
34B20 Weyl theory and its generalizations for ordinary differential equations
34L99 Ordinary differential operators
34B27 Green’s functions for ordinary differential equations
70H05 Hamilton’s equations


Zbl 0683.34008
Full Text: DOI