Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Sturmian comparison theorem for half-linear second-order differential equations

Horng Jaan Lia1 and Cheh Chih Yeha2

a1 Chienkuo Junior College of Technology and Commerce, Chang-Hua, Taiwan, Repubic of China

a2 Department of Mathematics, National Central University, Chung-Li, Taiwan, Republic of China


Let φ:ℝ→ℝ be defined by φ(s) = |s|p−2s, with p > 1 a fixed number. We extend Sturm Comparison Theorem of the linear differential equation


to the nonlinear differential equation


by using the Wirtinger inequality. A Lyapunov inequality and some oscillation criteria of (E) are also given.

(Received March 08 1994)

(Revised July 01 1994)