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The Nonlinear Limit-Point/Limit-Circle Problem for Higher Order Equations

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Miroslav Bartusek, Zuzana Dosla and John R. Graef
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** Address.**
M. Bartusek, Z. Dosla, Department of Mathematics, Masaryk University,
Janackovo nam. 2a, 662 95 Brno, Czech Republic

J. R. Graef, Department of Mathematics and Statistics, Mississippi State University,
Mississippi State, MS 39762, USA

** E-mail:**
bartusek@math.muni.cz

dosla@math.muni.cz

graef@math.msstate.edu

**Abstract.**
We describe the nonlinear limit-point/limit-circle problem for the
$n$-th order differential equation
$$ y^{(n)} + r(t)f(y,y', \dots , y^{(n-1)}) = 0. $$
The results are then applied to higher order linear and nonlinear equations.
A discussion of fourth order equations is included, and some directions for
further research are indicated.

**AMS classification.**
34C10, 34C15, 34B15

**Key words.**
Higher order equations, nonlinear limit-point,
nonlinear limit-circle