Oscillation constants for Euler type differential equations involving the \(p(t)\)-Laplacian
type: Item
instance of: scholarly article
title: Oscillation constants for Euler type differential equations involving the \(p(t)\)-Laplacian
zbMATH Open document ID: 1405.34029
author: Kōdai Fujimoto
author: Naoto Yamaoka
published in: Journal of Mathematical Analysis and Applications
publication date: 2018-12-10T00:00:00Z
review text: Oscillation problems are studied for the half-linear differential equation \[ (|x'|^{p(t)-2}x')'+\frac{\lambda}{t^{p(t)}}|x|^{p(t)-2}x=0 \] with \(p(t) > 1\). The main results are under the assumption that \(p(t)\) is non-decreasing and there exist \(p_\ast> 1\) and \(M > 0\) such that \(t^{|p_\ast-p(t)|} < M\) (i.e., \(\lim_{t\to\infty} p(t)=p_\ast\)). Using the notation \(\gamma(p)=((p-1)/p)^p\), the authors show that (a) If \(0<M<e\) and \(\lambda>\gamma(p_\ast)\), then all solutions of the equation are oscillatory; (b) If \(\lambda<\gamma(p_\ast)\), then the equation has a nonoscillatory solution. Further results are obtained for the case that \(\lim_{t\to\infty} p(t)=\infty\).
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 6991328
zbMATH Keywords: oscillation theory
zbMATH Keywords: oscillation constant
zbMATH Keywords: \(p(t)\)-Laplacian
zbMATH Keywords: half-linear differential equation
zbMATH Keywords: Riccati technique
reviewed by: Qingkai Kong
MaRDI profile type: Publication
full work available at URL: j.jmaa.2018.10.063
OpenAlex ID: W2898604269
cites work: Convergence analysis for a finite element approximation of a steady model for electrorheological fluids
cites work: On intermediate solutions and the Wronskian for half-linear differential equations
cites work: Lebesgue and Sobolev spaces with variable exponents
cites work: Power comparison theorems in half-linear oscillation theory
cites work: Q5466246
cites work: Oscillation and non-oscillation of Euler type half-linear differential equations
cites work: Oscillation constants for second-order ordinary differential equations related to elliptic equations with \(p\)-Laplacian
cites work: Perturbed generalized half-linear Riemann–Weber equation – further oscillation results
cites work: Overview of differential equations with non-standard growth
cites work: Conditional oscillation of half-linear differential equations with coefficients having mean values
cites work: Q5446482
cites work: Critical oscillation constant for Euler type half-linear differential equation having multi-different periodic coefficients
cites work: Asymptotic formulas for nonoscillatory solutions of conditionally oscillatory half-linear equations
cites work: On the modeling of electrorheological materials
cites work: Oscillation of nonlinear elliptic inequalities with p(x)-Laplacian
cites work: Oscillation criteria for half-linear differential equations with p(t)-Laplacian
cites work: Oscillation criteria for nonlinear differential equations with \(p(t)\)-Laplacian.
cites work: Comparison theorems for oscillation of second order half-linear differential equations
cites work: Oscillatory property of solutions for \(p(t)\)-Laplacian equations
Wikidata QID: Q129077634
DOI: 10.1016/J.JMAA.2018.10.063
description: scientific article; zbMATH DE number 6991328