Monotonicity properties of oscillatory solutions of differential equation ( a ( t ) | y ' | p - 1 y ' ) ' + f ( t , y , y ' ) = 0

Miroslav Bartušek; Chrysi G. Kokologiannaki

Archivum Mathematicum (2013)

  • Volume: 049, Issue: 3, page 199-207
  • ISSN: 0044-8753

Abstract

top
We obtain monotonicity results concerning the oscillatory solutions of the differential equation ( a ( t ) | y ' | p - 1 y ' ) ' + f ( t , y , y ' ) = 0 . The obtained results generalize the results given by the first author in [1] (1976). We also give some results concerning a special case of the above differential equation.

How to cite

top

Bartušek, Miroslav, and Kokologiannaki, Chrysi G.. "Monotonicity properties of oscillatory solutions of differential equation $(a(t)\vert y^{\prime }\vert ^{p-1}y^{\prime })^{\prime }+f(t,y,y^{\prime })=0$." Archivum Mathematicum 049.3 (2013): 199-207. <http://eudml.org/doc/260737>.

@article{Bartušek2013,
abstract = {We obtain monotonicity results concerning the oscillatory solutions of the differential equation $(a(t)\vert y^\{\prime \}\vert ^\{p-1\}y^\{\prime \})^\{\prime \}+f(t,y,y^\{\prime \})=0$. The obtained results generalize the results given by the first author in [1] (1976). We also give some results concerning a special case of the above differential equation.},
author = {Bartušek, Miroslav, Kokologiannaki, Chrysi G.},
journal = {Archivum Mathematicum},
keywords = {monotonicity; oscillatory solutions; monotonicity; oscillatory solutions},
language = {eng},
number = {3},
pages = {199-207},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Monotonicity properties of oscillatory solutions of differential equation $(a(t)\vert y^\{\prime \}\vert ^\{p-1\}y^\{\prime \})^\{\prime \}+f(t,y,y^\{\prime \})=0$},
url = {http://eudml.org/doc/260737},
volume = {049},
year = {2013},
}

TY - JOUR
AU - Bartušek, Miroslav
AU - Kokologiannaki, Chrysi G.
TI - Monotonicity properties of oscillatory solutions of differential equation $(a(t)\vert y^{\prime }\vert ^{p-1}y^{\prime })^{\prime }+f(t,y,y^{\prime })=0$
JO - Archivum Mathematicum
PY - 2013
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 049
IS - 3
SP - 199
EP - 207
AB - We obtain monotonicity results concerning the oscillatory solutions of the differential equation $(a(t)\vert y^{\prime }\vert ^{p-1}y^{\prime })^{\prime }+f(t,y,y^{\prime })=0$. The obtained results generalize the results given by the first author in [1] (1976). We also give some results concerning a special case of the above differential equation.
LA - eng
KW - monotonicity; oscillatory solutions; monotonicity; oscillatory solutions
UR - http://eudml.org/doc/260737
ER -

References

top
  1. Bartušek, M., Monotonicity theorems concerning differential equations y ' ' + f ( t , y , y ' ) = 0 , Arch. Math. (Brno) 12 (4) (1976), 169–178. (1976) MR0430410
  2. Bartušek, M., Monotonicity theorems for second order non-linear differential equations, Arch. Math. (Brno) 16 (3) (1980), 127–136. (1980) MR0594458
  3. Bartušek, M., On properties of oscillatory solutions of nonlinear differential equations of the n -th order, Diff. Equat. and Their Appl., Equadiff 6, vol. 1192, Lecture Notes in Math., Berlin, 1985, pp. 107–113. (1985) 
  4. Bartušek, M., On oscillatory solutions of differential inequalities, Czechoslovak Math. J. 42 (117) (1992), 45–52. (1992) Zbl0756.34033MR1152168
  5. Bartušek, M., Singular solutions for the differential equation with p -Laplacian, Arch. Math. (Brno) 41 (2005), 123–128. (2005) Zbl1116.34325MR2142148
  6. Bartušek, M., Došlá, Z., Cecchi, M., Marini, M., 10.1016/j.jmaa.2005.06.057, J. Math. Anal. Appl. 320 (2006), 108–120. (2006) Zbl1103.34016MR2230460DOI10.1016/j.jmaa.2005.06.057
  7. Došlá, Z., Cecchi, M., Marini, M., On second order differential equations with nonhomogenous Φ –Laplacian, Boundary Value Problems 2010 (2010), 17pp., ID 875675. (2010) MR2595170
  8. Došlá, Z., Háčik, M., Muldon, M. E., Further higher monotonicity properties of Sturm-Liouville function, Arch. Math. (Brno) 29 (1993), 83–96. (1993) MR1242631
  9. Došlý, O., Řehák, P., Half-linear differential equations, Elsevier, Amsterdam, 2005. (2005) Zbl1090.34001MR2158903
  10. Kiguradze, I., Chanturia, T., Asymptotic properties of solutions of nonautonomous ordinary differential equations, Kluwer, Dordrecht, 1993. (1993) Zbl0782.34002
  11. Lorch, L., Muldon, M. E., Szego, P., 10.4153/CJM-1970-142-1, Canad. J. Math. 22 (1970), 1238–1265. (1970) MR0274845DOI10.4153/CJM-1970-142-1
  12. Mirzov, J. D., Asymptotic properties of solutions of systems of nonlinear nonautonomous ordinary differential equations, Folia Fac. Sci. Natur. Univ. Masaryk. Brun. Math., Masaryk University, Brno, 2001. (2001) MR2144761
  13. Naito, M., Existence of positive solutions of higher-order quasilinear ordinary differential equations, Ann. Mat. Pura Appl. (4) 186 (2007), 59–84. (2007) Zbl1232.34054MR2263331
  14. Rohleder, M., On the existence of oscillatory solutions of the second order nonlinear ODE, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 51 (2) (2012), 107–127. (2012) Zbl1279.34050MR3058877

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.