Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1184.34043
Pašić, Mervan; Wong, James S.W.
Rectifiable oscillations in second-order half-linear differential equations. (English)
[J] Ann. Mat. Pura Appl. (4) 188, No. 3, 517-541 (2009). ISSN 0373-3114; ISSN 1618-1891/e

The authors continue their investigation of geometric aspects of oscillation theory of various second order differential equations [see, e.g. {\it M. Pašić} and {\it 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.
[Ondřej Došlý (Brno)]

MSC 2000:: *34C10 Qualitative theory of oscillations of ODE: Zeros, etc.

Keywords: oscillations; nonlinear equations; graph; rectifiability; fractal dimension; Minkowski content; asymptotics; perturbation

Citations: Zbl 1160.26304

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]