Journal of Inequalities and Applications 
Volume 6 (2001), Issue 4, Pages 387-404
doi:10.1155/S1025583401000236

Picone-type inequalities for nonlinear elliptic equations and their applications

Jaroslav Jaroš,1 Kusano Takaŝi,2 and Norio Yoshida3

 1Department of Mathematical Analysis, Faculty of Mathematics and Physics, Comenius University, Bratislava 842 15 , Slovakia
2Department of Applied Mathematics, Faculty of Science, Fukuoka University, Fukuoka 814-0180, Japan
3Department of Mathematics, Faculty of Science, Toyama University, Toyama 930-8555, Japan
Received 2 November 1999; Revised 24 January 2000

Abstract

Picone-type inequalities are derived for nonlinear elliptic equations, and Sturmian comparison theorems are established as applications. Oscillation theorems for forced super-linear elliptic equations and superlinear-sublinear elliptic equations are also obtained.