Geodesic
Estimations of noncontinuable solutions of second order differential equations with $p$-Laplacian
Archivum mathematicum, Tome 46 (2010) no. 2, pp. 135-144 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 34A12, 34C11
Keywords: second order differential equation; $p$-Laplacian; asymptotic properties; lower estimate; singular solution 
@article{ARM_2010_46_2_a5,
     author = {Pek\'arkov\'a, Eva},
     title = {Estimations of noncontinuable solutions of second order differential equations with $p${-Laplacian}},
     journal = {Archivum mathematicum},
     pages = {135--144},
     year = {2010},
     volume = {46},
     number = {2},
     mrnumber = {2684255},
     zbl = {1240.34187},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2010_46_2_a5/}
}
TY  - JOUR
AU  - Pekárková, Eva
TI  - Estimations of noncontinuable solutions of second order differential equations with $p$-Laplacian
JO  - Archivum mathematicum
PY  - 2010
SP  - 135
EP  - 144
VL  - 46
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/ARM_2010_46_2_a5/
LA  - en
ID  - ARM_2010_46_2_a5
ER  - 
%0 Journal Article
%A Pekárková, Eva
%T Estimations of noncontinuable solutions of second order differential equations with $p$-Laplacian
%J Archivum mathematicum
%D 2010
%P 135-144
%V 46
%N 2
%U http://geodesic.mathdoc.fr/item/ARM_2010_46_2_a5/
%G en
%F ARM_2010_46_2_a5
Pekárková, Eva. Estimations of noncontinuable solutions of second order differential equations with $p$-Laplacian. Archivum mathematicum, Tome 46 (2010) no. 2, pp. 135-144. http://geodesic.mathdoc.fr/item/ARM_2010_46_2_a5/

[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.

[2] Bartušek, M.: On noncontinuable solutions of $n$-th order differential equations. DCDIS A, Supplement, to appear. | MR

[3] Bartušek, M.: On existence of singular solution of $n$-th order differential equations. Arch. Math. (Brno) 36 (2000), 395–404. | MR

[4] Bartušek, M.: On existence unbounded noncontinuable solutions. Ann. Mat. Pura Appl. (4) 185 (2006), 93–107. | MR

[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.

[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. | MR | Zbl

[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. | MR | Zbl

[8] Bartušek, M., Osička, J.: On existence of singular solutions. Georgian Math. J. 8 (2001), 669–681. | MR

[9] Bartušek, M., Pekárková, E.: On existence of proper solutions of quasilinear second order differential equations. EJQTD 1 (2007), 1–14. | Zbl

[10] Bartušková, I.: Problem of Computations of Sewerage Systems. Ph.D. thesis, FAST Technical University Brno, 1997, in Czech.

[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

[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

[13] Kiguradze, I. T., Chanturia, T.: Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations. Dordrecht, Kluwer, 1993. | Zbl

[14] Medveď, M., Pekárková, E.: Existence of global solutions of systems of second order differential equations with $p$-Laplacian. EJDE 136 (2007), 1–9.

[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