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