A note on the oscillation problems for differential equations with p ( t ) -Laplacian

Kōdai Fujimoto

Archivum Mathematicum (2023)

  • Volume: 059, Issue: 1, page 39-45
  • ISSN: 0044-8753

Abstract

top
This paper deals with the oscillation problems on the nonlinear differential equation ( a ( t ) | x ' | p ( t ) - 2 x ' ) ' + b ( t ) | x | λ - 2 x = 0 involving p ( t ) -Laplacian. Sufficient conditions are given under which all proper solutions are oscillatory. In addition, we give a-priori estimates for nonoscillatory solutions and propose an open problem.

How to cite

top

Fujimoto, Kōdai. "A note on the oscillation problems for differential equations with $p(t)$-Laplacian." Archivum Mathematicum 059.1 (2023): 39-45. <http://eudml.org/doc/298995>.

@article{Fujimoto2023,
abstract = {This paper deals with the oscillation problems on the nonlinear differential equation $(a(t)|x^\{\prime \}|^\{p(t)-2\}x^\{\prime \})^\{\prime \}+b(t)|x|^\{\lambda -2\}x=0$ involving $p(t)$-Laplacian. Sufficient conditions are given under which all proper solutions are oscillatory. In addition, we give a-priori estimates for nonoscillatory solutions and propose an open problem.},
author = {Fujimoto, Kōdai},
journal = {Archivum Mathematicum},
keywords = {oscillation; $p(t)$-Laplacian; half-linear differential equations},
language = {eng},
number = {1},
pages = {39-45},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {A note on the oscillation problems for differential equations with $p(t)$-Laplacian},
url = {http://eudml.org/doc/298995},
volume = {059},
year = {2023},
}

TY - JOUR
AU - Fujimoto, Kōdai
TI - A note on the oscillation problems for differential equations with $p(t)$-Laplacian
JO - Archivum Mathematicum
PY - 2023
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 059
IS - 1
SP - 39
EP - 45
AB - This paper deals with the oscillation problems on the nonlinear differential equation $(a(t)|x^{\prime }|^{p(t)-2}x^{\prime })^{\prime }+b(t)|x|^{\lambda -2}x=0$ involving $p(t)$-Laplacian. Sufficient conditions are given under which all proper solutions are oscillatory. In addition, we give a-priori estimates for nonoscillatory solutions and propose an open problem.
LA - eng
KW - oscillation; $p(t)$-Laplacian; half-linear differential equations
UR - http://eudml.org/doc/298995
ER -

References

top
  1. Bartušek, M., Fujimoto, K., 10.1016/j.jde.2020.08.046, J. Differential Equations 269 (2020), 11646–11666. (2020) MR4152220DOI10.1016/j.jde.2020.08.046
  2. Berselli, L.C., Breit, D., Diening, L., 10.1007/s00211-015-0735-4, Numer. Math. 132 (2016), 657–689. (2016) MR3474486DOI10.1007/s00211-015-0735-4
  3. Chanturia, T.A., On singular solutions of strongly nonlinear systems of ordinary differential equations, Function theoretic methods in differential equations, Res. Notes in Math., no. 8, Pitman, London, 1976, pp. 196–204. (1976) 
  4. Došlá, Z., Fujimoto, K., 10.1142/S0219199721500462, Commun. Contemp. Math. 24 (2022), 1–22, No. 2150046. (2022) MR4508281DOI10.1142/S0219199721500462
  5. Došlá, Z., Marini, M., 10.1016/j.jmaa.2014.02.052, J. Math. Anal. Appl. 416 (2014), 497–510. (2014) MR3188719DOI10.1016/j.jmaa.2014.02.052
  6. Došlá, Z., Marini, M., Monotonicity conditions in oscillation to superlinear differential equations, Electron. J. Qual. Theory Differ. Equ. 2016 (2016), 1–13, No. 54. (2016) MR3533264
  7. Došlý, O., Řehák, P., Half-Linear Differential Equations, North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam, 2005. (2005) MR2158903
  8. Fujimoto, K., 10.1007/s10474-020-01034-5, Acta Math. Hungar. 162 (2020), 333–344. (2020) MR4169028DOI10.1007/s10474-020-01034-5
  9. Fujimoto, K., Yamaoka, N., 10.1016/j.jmaa.2018.10.063, J. Math. Anal. Appl. 470 (2019), 1238–1250. (2019) MR3870613DOI10.1016/j.jmaa.2018.10.063
  10. Harjulehto, P., Hästö, P., Lê, Ú.V., Nuortio, M., 10.1016/j.na.2010.02.033, Nonlinear Anal. 72 (2010), 4551–4574. (2010) Zbl1188.35072MR2639204DOI10.1016/j.na.2010.02.033
  11. Kiguradze, I.T., Chanturia, T.A., Asymptotic properties of solutions of nonautonomous ordinary differential equations, Kluwer Academic Publishers Group, Dordrecht, 1993. (1993) Zbl0782.34002
  12. Kitano, M., Kusano, T., 10.32917/hmj/1206127714, Hiroshima Math. J. 25 (1995), 321–355. (1995) DOI10.32917/hmj/1206127714
  13. Mehta, B.N., Aris, R., 10.1016/0022-247X(71)90043-6, J. Math. Anal. Appl. 36 (1971), 611–621. (1971) DOI10.1016/0022-247X(71)90043-6
  14. Rajagopal, K.R., Růžička, M., 10.1016/0093-6413(96)00038-9, Mech. Res. Comm. 23 (1996), 401–407. (1996) DOI10.1016/0093-6413(96)00038-9
  15. Şahiner, Y., Zafer, A., 10.1080/17476933.2012.686493, Complex Var. Elliptic Equ. 58 (2013), 537–546. (2013) MR3038745DOI10.1080/17476933.2012.686493
  16. Shoukaku, Y., Oscillation criteria for half-linear differential equations with p ( t ) -Laplacian, Differ. Equ. Appl. 6 (2014), 353–360. (2014) MR3265452
  17. Shoukaku, Y., 10.21136/MB.2016.5, Math. Bohem. 141 (2016), 71–81. (2016) MR3475138DOI10.21136/MB.2016.5
  18. Zhang, Q., 10.1155/2007/58548, J. Inequal. Appl. 2007 (2007), 1–8, 58548. (2007) MR2335972DOI10.1155/2007/58548

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.