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On the limit-point classification of a class of non-self-adjoint ordinary differential operators. (English) Zbl 0539.34018

See the preview in Zbl 0505.34022.

MSC:

34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations

Citations:

Zbl 0505.34022
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[1] Atkinson, F. V.; Evans, W. D., On solutions of a differential equation which are not of integrable square, Math. Z., 127, 323-332 (1972) · Zbl 0226.34026
[2] Brown, G. E., Unified Theory of Nuclear Models and Forces (1967), North-Holland: North-Holland Amsterdam
[3] Dolph, C. L., Recent developments in some non-selfadjoint problems of mathematical physics, Bull. Amer. Math. Soc., 67, 1-69 (1961) · Zbl 0099.07802
[4] Dunford, N.; Schwartz, J. T., Linear Operators II: Spectral Theory (1963), Interscience: Interscience New York
[5] Evans, W. D., On the limit-point, limit-circle classification of a second-order differential equation with a complex coefficient, J. London Math. Soc. (2), 4, 245-256 (1971) · Zbl 0229.34023
[6] Frentzen, H., Limit-point criteria for systems of differential equations, (Proc. Roy. Soc. Edinburgh Sect. A, 85 (1980)), 233-245, (3-4) · Zbl 0424.34031
[7] Galindo, A., On the existence of \(J\)-selfadjoint extensions of \(J\)-symmetric operators with adjoint, Comm. Pure Appl. Math., 15, 423-425 (1962) · Zbl 0109.08701
[8] Glazman, I. M., Direct Methods of Qualitative Spectral Analysis of Singular Differential Operators (1965), Israel Program for Scientific Translations: Israel Program for Scientific Translations Jerusalem · Zbl 0143.36505
[9] Goldberg, S., Unbounded Linear Operators (1966), McGraw-Hill: McGraw-Hill New York
[10] Kauffman, R. M., On the limit-\(n\) classification of ordinary differential operators with positive coefficients, (Proc. London Math. Soc. (3), 35 (1977)), 496-526 · Zbl 0382.47025
[11] Kauffman, R. M.; Read, T. T.; Zettl, A., The Deficiency Index Problem for Powers of Ordinary Differential Expressions, (Lecture Notes in Mathematics No. 621 (1977), Springer-Verlag: Springer-Verlag Berlin/New York) · Zbl 0367.34014
[12] Knowles, I., On \(J\)-selfadjoint extensions of \(J\)-symmetric operators, (Proc. Amer. Math. Soc., 79 (1980)), 42-44 · Zbl 0443.47035
[13] Knowles, I., On the boundary conditions characterizing \(J\)-selfadjoint extensions of \(J\)-symmetric operators, J. Differential Equations, 40, 217-231 (1981)
[14] Knowles, I.; Race, D., On the point spectra of complex Sturm-Liouville operators, (Proc. Roy. Soc. Edinburgh Sect. A, 85 (1980)), 263-289, (3-4) · Zbl 0446.47035
[15] McLeod, J. B., Square-integrable solutions of a second-order differential equation with complex coefficients, Quart. J. Math. Oxford Ser. (2), 13, 129-133 (1962) · Zbl 0133.34104
[16] Read, T. T., A limit-point criterion for expressions with oscillatory coefficients, Pacific J. Math., 66, 243-255 (1976) · Zbl 0355.34011
[17] Reed, M.; Simon, B., Methods of Modern Mathematical Physics II: Fourier Analysis, Self-Adjointness (1975), Academic Press: Academic Press New York · Zbl 0308.47002
[18] Sims, A. R., Secondary conditions for linear differential operators of the second order, J. Math. Mech., 6, 247-285 (1957) · Zbl 0077.29201
[19] Showalter, R. E., Hubert Space Methods for Partial Differential Equations (1977), Pitman: Pitman London · Zbl 0364.35001
[20] Úlehla, I.; Gomolčák, L.; Pluhař, Z., Optimal Model of the Atomic Nucleus (1964), Academic Press: Academic Press New York
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