Electronic Journal of Differential Equations, Vol. 2002(2002), No. 34, pp. 1-12. Title: Constants in the oscillation theory of higher order Sturm-Liouville differential equations Author: Ondrej Dosly (Masaryk University, Czech Republic) Abstract: We find the the exact value of a constant in some oscillation criteria for the higher order Sturm-Liouville differential equation $$ (-1)^{n}(t^\alpha y^{(n)})^{(n)}=q(t)y . $$ We also study some general aspects in the oscillation theory of this equation. Submitted October 25, 2001. Published April 4, 2002. Math Subject Classifications: 34C10 Key Words: Sturm-Liouville differential equation, variational method, oscillation and non-oscillation criteria, conditional oscillation. This and other articles are avilable in DVI, PDF, PS, and TeX format. Thanks to the European Mathematical Information Service, the EJDE and other journals have mirror copies through the world. Here is a partial listing of mirror sites. EUROPE: http://www.emis.de/journals/EJDE NORTH AMERICA: http://ejde.math.swt.edu http://ejde.math.unt.edu ftp: ejde.math.swt.edu (login: ftp) SOUTH AMERICA: http://www.icfes.gov.co/revistas/EJDE http://www.mat.unb.br/EMIS/journals/EJDE ASIA: http://www.kurims.kyoto-u.ac.jp/EMIS/journals/EJDE http://emis.math.ecnu.edu.cn/journals/EJDE AUSTRALIA: http://emis.maths.adelaide.edu.au/EMIS/journals/EJDE