# Article

 Title: Estimations of noncontinuable solutions of second order differential equations with $p$-Laplacian (English) Author: Pekárková, Eva Language: English Journal: Archivum Mathematicum ISSN: 0044-8753 (print) ISSN: 1212-5059 (online) Volume: 46 Issue: 2 Year: 2010 Pages: 135-144 Summary lang: English . Category: math . Summary: We study asymptotic properties of solutions for a system of second differential equations with $p$-Laplacian. The main purpose is to investigate lower estimates of singular solutions of second order differential equations with $p$-Laplacian $(A(t)\Phi _{p}(y^{\prime }))^{\prime }+B(t)g(y^{\prime })+R(t)f(y)=e(t)$. Furthermore, we obtain results for a scalar equation. (English) Keyword: second order differential equation Keyword: $p$-Laplacian Keyword: asymptotic properties Keyword: lower estimate Keyword: singular solution MSC: 34A12 MSC: 34C11 idZBL: Zbl 1240.34187 idMR: MR2684255 . Date available: 2010-06-22T22:11:55Z Last updated: 2013-09-19 Stable URL: http://hdl.handle.net/10338.dmlcz/140309 . Reference: [1] Astašova, I. V.: On asymptotic behaviour of solutions of nonlinear differential equations.Dokl. Semin. Inst. Prikl. Mat. im. I. N. Vekua 1 (3) (1985), 9–11. Reference: [2] Bartušek, M.: On noncontinuable solutions of $n$-th order differential equations.DCDIS A, Supplement, to appear. MR 2518879 Reference: [3] Bartušek, M.: On existence of singular solution of $n$-th order differential equations.Arch. Math. (Brno) 36 (2000), 395–404. MR 1822807 Reference: [4] Bartušek, M.: On existence unbounded noncontinuable solutions.Ann. Mat. Pura Appl. (4) 185 (2006), 93–107. MR 2187756 Reference: [5] Bartušek, M., Graef, J. R.: Strong nonlinear limit-point/limit-circle problem for second order nonlinear equations.Nonlinear Stud. 9 (1) (2006), 361–369. Reference: [6] Bartušek, M., Graef, J. R.: The strong nonlinear limit-point/limit-circle properties for a class of even order equations.Comm. Appl. Nonlinear Anal. 15 (3) (2008), 29–45. Zbl 1165.34325, MR 2441804 Reference: [7] Bartušek, M., Medveď, M.: Existence of global solutions for systems of second-order functional-differential equations with $p$-Laplacian.EJDE 40 (2008), 1–8. Zbl 1171.34335, MR 2392944 Reference: [8] Bartušek, M., Osička, J.: On existence of singular solutions.Georgian Math. J. 8 (2001), 669–681. MR 1884492 Reference: [9] Bartušek, M., Pekárková, E.: On existence of proper solutions of quasilinear second order differential equations.EJQTD 1 (2007), 1–14. Zbl 1115.34032 Reference: [10] Bartušková, I.: Problem of Computations of Sewerage Systems.Ph.D. thesis, FAST Technical University Brno, 1997, in Czech. Reference: [11] Chanturia, T.: On existence of singular and unbounded oscillatory solutions of differential equations of Emden-Fowler type.Differ. Uravn. 28 (1992), 1009–1022. MR 1198158 Reference: [12] Jaroš, J., Kusano, T.: On black hole solutions of second order differential equation with singularity in the diffential operator.Funkcial. Ekvac. 43 (2000), 491–509. MR 1815473 Reference: [13] Kiguradze, I. T., Chanturia, T.: Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations.Dordrecht, Kluwer, 1993. Zbl 0782.34002 Reference: [14] Medveď, M., Pekárková, E.: Existence of global solutions of systems of second order differential equations with $p$-Laplacian.EJDE 136 (2007), 1–9. Reference: [15] Mirzov, J. D.: Asymptotic Properties of Solutions of System of Nonlinear Nonautonomous Differential Equations.Folia Fac. Sci. Natur. Univ. Masaryk. Brun. Math. 14 (2004). MR 2144761 .

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