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Hamiltonian systems of limit point or limit circle type with both endpoints singular. (English) Zbl 0476.34027


MSC:

34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34B99 Boundary value problems for ordinary differential equations
70H05 Hamilton’s equations
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[1] Atkinson, F. V., Discrete and Continuous Boundary Problems (1964), Academic Press: Academic Press New York · Zbl 0117.05806
[2] Coddington, E. A.; Levinson, N., Theory of Ordinary Differential Equations (1955), McGraw-Hill: McGraw-Hill New York · Zbl 0042.32602
[3] Coppel, W. A., Disconjugacy, (Lecture Notes in Mathematics No. 220 (1971), Springer-Verlag: Springer-Verlag Berlin/New York) · Zbl 0224.34003
[4] Fulton, C. T., Parameterizations of Titchmarsch’s \(m\)(λ)-functions in the limit circle case, Trans. Amer. Math. Soc., 229, 51-63 (1977) · Zbl 0358.34021
[5] Hille, E., Lectures on Ordinary Differential Equations (1969), Addison-Wesley: Addison-Wesley Reading, Massachusetts · Zbl 0179.40301
[6] Hinton, D. B.; Shaw, J. K., On Titchmarsh-Weyl \(m\)(λ)-functions for linear Hamiltonian systems, J. Differential Equations, 40, 3, 316-342 (1981) · Zbl 0472.34014
[7] Hinton, D. B.; Shaw, J. K., On the spectrum of a singular Hamiltonian system, Quaestiones Math., 5, 29-81 (1982) · Zbl 0509.34018
[8] Hinton, D. B.; Shaw, J. K., Titchmarsh-Weyl theory for Hamiltonian systems, (Knowles, I. W.; Lewis, R. T., Spectral Theory of Differential Operators (1981), North-Holland: North-Holland New York/Amsterdam), 219-231 · Zbl 0472.34014
[9] Hinton, D. B.; Shaw, J. K., Parameterization of the \(m(λ)\) function for a Hamiltonian system of limit circle type, (Proc. Roy. Soc. Edinburgh Sect. A, 93 (1983)), 349-360 · Zbl 0532.34011
[11] Kodaira, K., The eigenvalue problem for ordinary differential equations of the second order and Heisenberg’s theory of \(S\)-matrices, Amer. J. Math., 71, 921-945 (1949) · Zbl 0035.27101
[12] Kogan, V. I.; Rofe-Beketov, F. S., On square-integrable solutions of symmetric systems of differential equations of arbitrary order, (Proc. Roy. Soc. Edinburgh Sect. A, 74 (1974)), 5-40 · Zbl 0333.34021
[13] Krall, A. M., Boundary values for an eigenvalue problem with a singular potential, J. Differential Equations, 45, 128-138 (1982) · Zbl 0457.35066
[14] Orlov, S. A., Nested matrix disks analytically depending on a parameter, and theorems on invariance of ranks of radii of limiting disks, Math. USSR-Izv., 10, 3, 565-613 (1976) · Zbl 0374.34015
[15] Stone, M. H., Linear Transformations in Hilbert Space and Their Applications to Analysis, (Amer. Math. Soc. Colloq. Publ., Vol. 15 (1932), Amer. Math. Society: Amer. Math. Society Providence, RI) · Zbl 0118.29903
[16] Titchmarsh, E. C., Eigenfunction Expansions Associated with Second-Order Differential Equations (1962), Oxford Univ. Press (Clarendon): Oxford Univ. Press (Clarendon) Oxford, Part I · Zbl 0099.05201
[17] Walker, P. W., Adjoint boundary value problems for compactified singular differential operators, Pacific J. Math., 49, 265-278 (1973) · Zbl 0287.34013
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