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

Miroslav Bartusek, Zuzana Dosla and John R. Graef

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


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