Power comparison theorems for oscillation problems for second order differential equations with p(t)-Laplacian

被引：0
作者：
K. Fujimoto
机构：
[1] Masaryk University,Department of Mathematics and Statistics
来源：
Acta Mathematica Hungarica | 2020年 / 162卷
关键词：
oscillation; comparison theorem; -Laplacian; half-linear differential equation; Riccati technique; primary 34C10; secondary 34C15;
D O I：
暂无
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学科分类号：
摘要：
This paper deals with the nonlinear differential equation (r(t)|x′|p(t)-2x′)′+c(t)|x|p(t)-2x=0,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(r(t)|x'|^{p(t)-2}x')'+c(t) |x|^{p(t)-2}x=0, $$\end{document} where r(t) > 0 and c(t) are continuous functions, and p(t) > 1 is a smooth function. We establish a comparison theorem for the oscillation problem for this equation with respect to the power p(t). Using our result, we can utilize oscillation criteria given for half-linear differential equations to equations with p(t)-Laplacian.
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页码：333 / 344
页数：11
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  • [1] Berselli LC(2016)Convergence analysis for a finite element approximation of a steady model for electrorheological fluids Numer. Math. 132 657-689
  • [2] Breit D(2008)A remark on power comparison theorem for half-linear differential equations Math. Bohem. 133 187-195
  • [3] Diening L(2013)Power comparison theorems in half-linear oscillation theory J. Math. Anal. Appl. 401 611-619
  • [4] Bognár G(2011)Critical oscillation constant for half-linear differential equations with periodic coefficients Ann. Mat. Pura Appl. 190 395-408
  • [5] Došlý O(2018)Integral averaging technique for oscillation of damped half-linear oscillators Czechoslovak Math. J. 68 755-770
  • [6] Došlý O(2019)Oscillation constants for Euler type differential equations involving the J. Math. Anal. Appl. 470 1238-1250
  • [7] Fišnarová S(2010)-Laplacian Nonlinear Anal. 72 4551-4574
  • [8] Mařík R(1996)Overview of differential equations with non-standard growth Mech. Res. Comm. 23 401-407
  • [9] Došlý O(2008)On the modeling of electrorheological materials Acta Math. Hungar. 121 93-105
  • [10] Hasil P(2013)Comparison of nonlinearities in oscillation theory of half-linear differential equations Complex Var. Elliptic Equ. 58 537-546
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