Picone-type inequality and Sturmian comparison theorems for quasilinear elliptic operators with p(x)-Laplacians

Abstract

A Picone-type inequality for quasilinear elliptic operators with mixed nonlinearities and with p(x)-Laplacian is established, and Sturmian comparison theorems are derived on the basis of the Picone-type inequality. Generalizations to more general quasilinear elliptic operators with p(x)-Laplacians and specializations to quasilinear ordinary differential operators with p(t)-Laplacians are shown.

Keywords

• p(x)-Laplacian
• Picone-type inequality
• quasilinear elliptic operators
• Sturmian comparison theorem
• mixed nonlinearities