Sturm comparison theorems for some elliptic type equations via Picone-tpye inequalities

Abstract

Sturm theorems have appeared as one of the fundamental subjects in qualitative theory to determine properties of the solutions of differential equations. Motivated by some recent developments for half-linear type elliptic equations, we obtain Picone-type inequalities for two pairs of elliptic type equations with damping and external terms in order to establish Sturmian comparison theorems. Some oscillation results are given as applications.

Keywords

• elliptic equations
• half-linear equations
• oscillation
• picone's inequality
• sturm theory