Necessary and sufficient conditions for nonoscillatory solutions of impulsive delay differential equations

Abstract

Monotonicity of solutions is an important property in the investigation of oscillatory behaviors of differential equations. A number of papers provide some existence criteria for eventually positive increasing solutions. However, relatively little attention is paid to eventually positive solutions that are also eventually decreasing solutions. For this reason, we establish several new and sharp oscillatory criteria for impulsive functional differential equations from this viewpoint.

Keywords

• impulsive differential equation
• delay
• positive solution
• comparaion theorem
• oscillation criteria