Estimations of noncontinuable solutions of second order differential equations with p -Laplacian

Eva Pekárková

Archivum Mathematicum (2010)

  • Volume: 046, Issue: 2, page 135-144
  • ISSN: 0044-8753

Abstract

top
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 ) Φ p ( y ' ) ) ' + B ( t ) g ( y ' ) + R ( t ) f ( y ) = e ( t ) . Furthermore, we obtain results for a scalar equation.

How to cite

top

Pekárková, Eva. "Estimations of noncontinuable solutions of second order differential equations with $p$-Laplacian." Archivum Mathematicum 046.2 (2010): 135-144. <http://eudml.org/doc/37773>.

@article{Pekárková2010,
abstract = {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.},
author = {Pekárková, Eva},
journal = {Archivum Mathematicum},
keywords = {second order differential equation; $p$-Laplacian; asymptotic properties; lower estimate; singular solution; second order differential equation; -Laplacian; asymptotic properties; lower estimate; singular solution},
language = {eng},
number = {2},
pages = {135-144},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Estimations of noncontinuable solutions of second order differential equations with $p$-Laplacian},
url = {http://eudml.org/doc/37773},
volume = {046},
year = {2010},
}

TY - JOUR
AU - Pekárková, Eva
TI - Estimations of noncontinuable solutions of second order differential equations with $p$-Laplacian
JO - Archivum Mathematicum
PY - 2010
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 046
IS - 2
SP - 135
EP - 144
AB - 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.
LA - eng
KW - second order differential equation; $p$-Laplacian; asymptotic properties; lower estimate; singular solution; second order differential equation; -Laplacian; asymptotic properties; lower estimate; singular solution
UR - http://eudml.org/doc/37773
ER -

References

top
  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. (1985) 
  2. Bartušek, M., On noncontinuable solutions of n -th order differential equations, DCDIS A, Supplement, to appear. MR2518879
  3. Bartušek, M., On existence of singular solution of n -th order differential equations, Arch. Math. (Brno) 36 (2000), 395–404. (2000) MR1822807
  4. Bartušek, M., On existence unbounded noncontinuable solutions, Ann. Mat. Pura Appl. (4) 185 (2006), 93–107. (2006) MR2187756
  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. (2006) 
  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. (2008) Zbl1165.34325MR2441804
  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. (2008) Zbl1171.34335MR2392944
  8. Bartušek, M., Osička, J., On existence of singular solutions, Georgian Math. J. 8 (2001), 669–681. (2001) MR1884492
  9. Bartušek, M., Pekárková, E., On existence of proper solutions of quasilinear second order differential equations, EJQTD 1 (2007), 1–14. (2007) Zbl1115.34032
  10. Bartušková, I., Problem of Computations of Sewerage Systems, Ph.D. thesis, FAST Technical University Brno, 1997, in Czech. (1997) 
  11. Chanturia, T., On existence of singular and unbounded oscillatory solutions of differential equations of Emden-Fowler type, Differ. Uravn. 28 (1992), 1009–1022. (1992) MR1198158
  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. (2000) MR1815473
  13. Kiguradze, I. T., Chanturia, T., Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations, Dordrecht, Kluwer, 1993. (1993) Zbl0782.34002
  14. Medveď, M., Pekárková, E., Existence of global solutions of systems of second order differential equations with p -Laplacian, EJDE 136 (2007), 1–9. (2007) 
  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). (2004) MR2144761

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.