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On boundary value problems for Hamiltonian systems with two singular points. (English) Zbl 0539.34016

A linear Hamiltonian system of differential equations is considered over an interval (a,b), where both endpoints are singular. The nesting property of matrix discs, the analogy of the Weyl circles, is used to construct solutions of integrable weighted square and thus the Green’s matrix for a singular problem. In the limit point case, the radius matrices \(R_ 1(\lambda)\) and \(R_ 2(\lambda)\) are shown to converge to 0, and this is used to prove that solutions of integrable weighted square satisfy Titchmarsh’s \(\lambda\)-dependent boundary condition at a singular endpoint.

MSC:

34B20 Weyl theory and its generalizations for ordinary differential equations
34L99 Ordinary differential operators
34B27 Green’s functions for ordinary differential equations
47E05 General theory of ordinary differential operators
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