Journal of Inequalities and Applications 
Volume 2006 (2006), Article ID 52378, 17 pages
doi:10.1155/JIA/2006/52378

Picone-type inequalities for nonlinear elliptic equations with first-order terms 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, University of Toyama, Toyama 930-8555, Japan
Received 24 February 2004; Revised 13 April 2004; Accepted 13 April 2004

Abstract

Picone-type inequalities are established for nonlinear elliptic equations which are generalizations of nonself-adjoint linear elliptic equations, and Sturmian comparison theorems are derived as applications. Oscillation results are also obtained for forced superlinear elliptic equations and superlinear-sublinear elliptic equations.