Rectifiable oscillations in second-order half-linear differential equations
type: Item
instance of: scholarly article
title: Rectifiable oscillations in second-order half-linear differential equations
zbMATH Open document ID: 1184.34043
author: Mervan Pašić
author: James S. W. Wong
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2009-10-02T00:00:00Z
review text: The authors continue their investigation of geometric aspects of oscillation theory of various second order differential equations [see, e.g. \textit{M. Pašić} and \textit{J. S. W. Wong}, Differ. Equ. Appl. 1, No. 1, 85--122 (2009; Zbl 1160.26304)]. In this paper, the main attention is devoted to the half-linear differential equation \[ (\Phi(y'))'+f(x)\Phi(y)=0,\quad \Phi(y):=|y|^{p-2}y,\;p>1, \tag{1} \] where \(x\in I:=(0,1]\), \(f\in C^2(I)\), \(f(x)>0\), and \(\lim_{x\to 0-} f(x) =\infty\). Integral criteria are established which guarantee that (1) is oscillatory for \(x\to 0-\) and that the graph of oscillatory solutions has finite/infinite arclength. Some other geometrical aspects of oscillation of (1), like the fractal dimension of graphs of its solutions, are investigated as well.
reviewed by: Ondřej Došlý
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 5610638
zbMATH Keywords: oscillations
zbMATH Keywords: nonlinear equations
zbMATH Keywords: graph
zbMATH Keywords: rectifiability
zbMATH Keywords: fractal dimension
zbMATH Keywords: Minkowski content
zbMATH Keywords: asymptotics
zbMATH Keywords: perturbation
MaRDI profile type: Publication
full work available at URL: s10231-008-0087-0
OpenAlex ID: W2027827154
cites work: Gradient estimates for thep(x)-Laplacean system
cites work: Q4650507
cites work: Q4748596
cites work: Q5533446
cites work: Q5703731
cites work: Q4750126
cites work: On the partial regularity of energy-minimizing, area-preserving maps
cites work: Q5330830
cites work: Q5288929
cites work: Rectifiable oscillations in second-order linear differential equations
cites work: Q4328334
cites work: Q3511021
cites work: Minkowski-Bouligand dimension of solutions of the one-dimensional \(p\)-Laplacian.
cites work: Rectifiable and unrectifiable oscillations for a class of second-order linear differential equations of Euler type
cites work: Fractal oscillations for a class of second order linear differential equations of Euler type
cites work: Q3605070
cites work: Q4023647
cites work: Equivalence between the growth of \(\int_{b(x,r)}| \nabla u| ^ pdy\) and T in the equation \(P[u]=T\)
cites work: Local Behavior of Solutions of Quasilinear Elliptic Equations With General Structure
cites work: Sturmian theory for ordinary differential equations
cites work: Electrorheological fluids: Modeling and mathematical theory
cites work: Q5584775
cites work: Q4317869
cites work: On rectifiable oscillation of Euler type second order linear differential equations
DOI: 10.1007/S10231-008-0087-0
description: scientific article; zbMATH DE number 5610638