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

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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

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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

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