IJPAM: Volume 45, No. 4 (2008)

NONLINEAR LIMIT-POINT/LIMIT-CIRCLE
PROPERTIES OF SOLUTIONS OF SECOND ORDER
DIFFERENTIAL EQUATIONS WITH $\boldsymbol{p}$-LAPLACIAN

Miroslav Bartušek$^1$, John R. Graef$^2$
$^1$Faculty of Science
Masaryk University Brno
Janáckovo Nám. 2a, Brno, 602 00, CZECH REPUBLIC
e-mail: bartusek@math.muni.cz
$^2$Department of Mathematics
The University of Tennessee at Chattanooga
735 Vice St., Chattanooga, TN 37403-2598, USA
e-mail: john-graef@utc.edu


Abstract.The authors consider the nonlinear differential equation

\begin{displaymath}
\big(a(t)\vert y'\vert^{p-1}y'\big)' + r(t)\, f(y)=0,
\end{displaymath}

where $p>0$, $a(t)>0$, $r(t)>0$, and $xf(x) > 0$ for $x \ne 0$ and prove some new nonlinear limit-point and nonlinear limit-circle results. Their results are illustrated with some examples.

Received: October 2, 2007

AMS Subject Classification: 34B20, 34C11, 34C15, 34D05

Key Words and Phrases: half-linear equations, $p$-Laplacian, nonlinear limit-circle, nonlinear limit-point, second order differential equations, strong nonlinear limit-circle, strong nonlinear limit-point

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 45
Issue: 4