Constants in the oscillation theory of higher order Sturm-Liouville differential equations

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.

Keywords

• Sturm-Liouville differential equation, variational method, oscillation and non-oscillation criteria, conditional oscillation.