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Limit-point/limit-circle results for equations with damping. (English) Zbl 1260.34053
Summary: The authors study the nonlinear limit-point and limit-circle properties for the second-order nonlinear damped differential equation $$(a(t)|y'|^{p-1}y')' + b(t)|y'|^{q-1}y' + r(t)|y|^{\lambda -1}y = 0,$$where $0 < \lambda \leq p \leq q$, $a(t) > 0$, and $r(t) > 0$. Some examples are given to illustrate the main results.
MSC:
34B20Weyl theory and its generalizations
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Full Text: DOI
References:
[1] M. Bartu\vsek and E. Pekárková, “On existence of proper solutions of quasilinear second order differential equations,” Electronic Journal of Qualitative Theory of Differential Equations, vol. 2007, no. 1, pp. 1-14, 2007. · Zbl 1115.34032 · http://www.math.u-szeged.hu/ejqtde/2007/200705.html
[2] M. Bartu\vsek, Z. Do\vslá, and J. R. Graef, The Nonlinear Limit-Point/Limit-Circle Problem, Birkhäuser, Boston, Mass, USA, 2004. · Zbl 1053.34024 · doi:10.1080/00036810310001632835
[3] M. Bartu\vsek and J. R. Graef, “Nonlinear limit-point/limit-circle properties of solutions of second order differential equations with p-Laplacian,” International Journal of Pure and Applied Mathematics, vol. 45, no. 4, pp. 501-518, 2008. · Zbl 1162.34020
[4] M. Bartu\vsek and J. R. Graef, “Strong nonlinear limit-point/limit-circle properties for forced Thomas-Fermi equations with p-Laplacian,” Panamerican Mathematical Journal, vol. 18, no. 1, pp. 73-88, 2008. · Zbl 1147.34020
[5] M. Bartu\vsek and J. R. Graef, “Asymptotic behavior of solutions of a differential equation with p-Laplacian and forcing term,” Differential Equations and Dynamical Systems, vol. 15, pp. 61-87, 2007. · Zbl 1165.34367
[6] M. Bartu\vsek and J. R. Graef, “The strong nonlinear limit-point/limit-circle properties for super-half-linear equations,” Panamerican Mathematical Journal, vol. 17, no. 1, pp. 25-38, 2007. · Zbl 1148.34023
[7] M. Bartu\vsek and J. R. Graef, “The strong nonlinear limit-point/limit-circle properties for sub-half-linear equations,” Dynamic Systems and Applications, vol. 15, no. 3-4, pp. 585-602, 2006.
[8] M. Bartu\vsek and J. R. Graef, “The strong limit-point property for Emden-Fowler equations,” Differential Equations and Dynamical Systems, vol. 14, no. 3-4, pp. 383-405, 2006. · Zbl 1138.34018
[9] M. Bartu\vsek and J. R. Graef, “Asymptotic properties of solutions of a forced second order differential equation with p-Laplacian,” Panamerican Mathematical Journal, vol. 16, no. 2, pp. 41-59, 2006. · Zbl 1103.34037
[10] 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
[11] M. Bartu\vsek and J. R. Graef, “Some limit-point and limit-circle results for second order Emden-Fowler equations,” Applicable Analysis, vol. 83, no. 5, pp. 461-476, 2004. · Zbl 1053.34024 · doi:10.1080/00036810310001632835
[12] 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
[13] J. R. Graef, “Limit circle type results for sublinear equations,” Pacific Journal of Mathematics, vol. 104, no. 1, pp. 85-94, 1983. · Zbl 0535.34024 · doi:10.2140/pjm.1983.104.85
[14] 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
[15] 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
[16] O. Do\vslý and P. \vRehák, Half-Linear Differential Equations, vol. 202 of North-Holland Mathematics Studies, Elsevier, Amsterdam, The Netherlands, 2005.
[17] J. Shao and W. Song, “Limit circle/limit point criteria for second-order sublinear differential equations with damping term,” Abstract and Applied Analysis, vol. 2011, Article ID 803137, 12 pages, 2011. · Zbl 1272.34034 · doi:10.1155/2011/803137
[18] L. Xing, W. Song, Z. Zhang, and Q. Xu, “Limit circle/limit point criteria for second-order superlinear differential equations with a damping term,” Journal of Applied Mathematics, vol. 2011, Article ID 361961, 11 pages, 2012. · Zbl 1244.34047 · doi:10.1155/2012/361961
[19] N. Dunford and J. T. Schwartz, Linear Operators; Part II: Spectral Theory, John Wiley & Sons, New York, NY, USA, 1963. · Zbl 0128.34803