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Limit circle/limit point criteria for second-order superlinear differential equations with a damping term. (English) Zbl 1244.34047
Summary: We establish some new criteria for the classifications of superlinear differential equations as being of the nonlinear limit circle type or of the nonlinear limit point type, generalizing some known results.

MSC:
34B20Weyl theory and its generalizations
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References:
[1] H. Weyl, “Über gewöhnliche differentialgleichungen mit singularitäten und die zugehörigen entwicklungen willkürlicher funktionen,” Mathematische Annalen, vol. 68, no. 2, pp. 220-269, 1910. · Zbl 41.0343.01 · doi:10.1007/BF01474161
[2] M. Bartu\vsek, Z. Doslá, and J. R. Graef, “On the definations of the nonlinear limit-point/limit-circle properties,” Differential Equations and Dynamical Systems, vol. 9, pp. 49-61, 2001. · Zbl 1231.34044
[3] J. R. Graef, “Limit circle type criteria for nonlinear differential equations,” Proceedings of the Japan Academy, Series A, vol. 55, no. 2, pp. 49-52, 1979. · Zbl 0428.34017 · doi:10.3792/pjaa.55.49
[4] J. R. Graef, “Limit circle criteria and related properties for nonlinear equations,” Journal of Differential Equations, vol. 35, no. 3, pp. 319-338, 1980. · Zbl 0441.34024 · doi:10.1016/0022-0396(80)90032-7
[5] J. R. Graef and P. W. Spikes, “On the nonlinear limit-point/limit-circle problem,” Nonlinear Analysis, vol. 7, no. 8, pp. 851-871, 1983. · Zbl 0535.34023 · doi:10.1016/0362-546X(83)90062-7
[6] P. W. Spikes, “Criteria of limit circle type for nonlinear differential equations,” SIAM Journal on Mathematical Analysis, vol. 10, no. 3, pp. 456-462, 1979. · Zbl 0413.34033 · doi:10.1137/0510042
[7] M. V. Fedoryuk, Asymptotic Analysis, Springer, Berlin, Germany, 1993. · Zbl 0782.34001
[8] P. Hartman and A. Wintner, “Criteria of non-degeneracy for the wave equation,” American Journal of Mathematics, vol. 70, pp. 295-308, 1948. · Zbl 0035.18201 · doi:10.2307/2372327
[9] M. Bartu\vsek and J. R. Graef, “The nonlinear limit-point/limit-circle problem for second order equations with p-Laplacian,” Dynamic Systems and Applications, vol. 14, no. 3-4, pp. 431-446, 2005. · Zbl 1098.34018
[10] M. Bartu\vsek, Z. Doslá, and J. R. Graef, “The nonlinear limitpoint/limit-circle problem,” Birkhauser, vol. 3, pp. 34-35, 2005.