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Limit circle criteria and related properties for nonlinear equations. (English) Zbl 0441.34024

MSC:
34C05Location of integral curves, singular points, limit cycles (ODE)
34A34Nonlinear ODE and systems, general
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References:
[1] Atkinson, F. V.: Nonlinear extensions of limit-point criteria. Math. Z. 130, 297-312 (1973) · Zbl 0273.34008
[2] Bellman, R.: Stability theory of differential equations. (1953) · Zbl 0053.24705
[3] Burlak, J.: On the non-existence of L2-solutions of nonlinear differential equations. Proc. Edinburgh math. Soc. 14, 257-268 (1965) · Zbl 0149.04403
[4] Burton, T. A.; Patula, W. T.: Limit circle results for second order equations. Monatsh. math. 81, 185-194 (1976) · Zbl 0339.34028
[5] Coppel, W. A.: Stability and asymptotic behavior of differential equations. (1965) · Zbl 0154.09301
[6] Detki, J.: The solvability of a certain second order nonlinear ordinary differential equation in $Lp(0, \infty)$. Math. balk. 4, 115-119 (1974) · Zbl 0318.34006
[7] Dunford, N.; Schwartz, J. T.: Linear operators, part II, spectral theory. (1963) · Zbl 0128.34803
[8] Everitt, W. N.: On the limit-circle classification of second-order differential expressions. Quart. J. Math. Oxford ser. 23, 193-196 (1972) · Zbl 0256.34028
[9] Graef, J. R.; Spikes, P. W.: Asymptotic behavior of solutions of a second order nonlinear differential equation. J. differential equations 17, 461-476 (1975) · Zbl 0298.34028
[10] Graef, J. R.; Spikes, P. W.: Asymptotic properties of solutions of a second order nonlinear differential equation. Publ. math. Debrecen 24, 39-51 (1977) · Zbl 0379.34036
[11] Grimmer, R. C.; Patula, W. T.: Nonoscillatory solutions of forced second-order linear equations. J. math. Anal. appl. 56, 452-459 (1976) · Zbl 0338.34030
[12] Hallam, T. G.: On the nonexistence of lp solutions of certain nonlinear differential equations. Glasgow math. J. 8, 133-138 (1967) · Zbl 0163.10602
[13] Hartman, P.; Wintner, A.: Criteria of non-degeneracy for the wave equation. Amer. J. Math. 70, 295-308 (1948) · Zbl 0035.18201
[14] Hinton, D.: Limit point-limit circle criteria for (py’)’ + $qy = {\lambda}$ky. Lecture notes in mathematics no. 415, 173-183 (1974) · Zbl 0337.34019
[15] 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) · Zbl 0367.34014
[16] Knowles, I.: On a limit-circle criterion for second-order differential operators. Quart. J. Math. Oxford ser. 24, 451-455 (1973) · Zbl 0271.34028
[17] Knowles, I.: On second-order differential operators of limit circle type. Lecture notes in mathematics no. 415, 184-187 (1974)
[18] Krall, A. M.: On the solutions of (ry’)’ + qy = f. Monatsh. math. 80, 115-118 (1975) · Zbl 0323.34029
[19] Kwong, M. K.: On boundedness of solutions of second order differential equations in the limit circle case. Proc. amer. Math. soc. 52, 242-246 (1975) · Zbl 0329.34021
[20] Levinson, N.: Criteria for the limit-point case for second order linear differential operators. Časopis pěst. Mat. 74, 17-20 (1949) · Zbl 0033.18102
[21] Patula, W. T.; Waltman, P.: Limit point classification of second order linear differential equations. J. London math. Soc. 8, 209-216 (1974) · Zbl 0309.34016
[22] Patula, W. T.; Wong, J. S. W: An lp-analogue of the Weyl alternative. Math. ann. 197, 9-28 (1972) · Zbl 0223.34054
[23] Spikes, P. W.: On the integrability of solutions of perturbed nonlinear differential equations. Proc. roy. Soc. Edinburgh sect. A 77, 309-318 (1977) · Zbl 0384.34035
[24] Suyemoto, L.; Waltman, P.: Extension of a theorem of A. Winter. Proc. amer. Math. soc. 14, 970-971 (1963) · Zbl 0127.31102
[25] Titchmarsh, E. C.: Eigenfunction expansions associated with second-order differential equations. (1946) · Zbl 0061.13505
[26] Titchmarsh, E. C.: On the uniqueness of the Green’s function associated with a second-order differential equation. Canad. J. Math. 1, 191-198 (1949) · Zbl 0031.30801
[27] Weyl, H.: Über gewöhnliche differentialgleichungen mit singularitäten und die zugehörige entwicklung willkürlicher funktionen. Math. ann. 68, 220-269 (1910) · Zbl 41.0343.01
[28] Wong, J. S. W: Remark on a theorem of A. Wintner. Enseignement math. 13, 103-106 (1967) · Zbl 0173.09903
[29] Wong, J. S. W: Remarks on the limit-circle classification of second-order differential operators. Quart. J. Math. Oxford 24, 423-425 (1973) · Zbl 0268.34031
[30] Wong, J. S. W: Square integrable solutions of lp perturbations of second order linear differential equations. Lecture notes in mathematics no. 415, 282-292 (1974)
[31] Wong, J. S. W: Square integrable solutions of perturbed linear differential equations. Proc. roy. Soc. Edinburgh sect. A 73, 251-254 (1974--1975) · Zbl 0333.34044
[32] Wong, J. S. W; Zettl, A.: On the limit point classification of second order differential equations. Math. Z. 132, 297-304 (1973) · Zbl 0257.34030