Extremal solutions of measure differential equations

Abstract

We investigate the existence of the least and greatest solutions to measure differential equations, as well as the relation between the extremal solutions and lower or upper solutions. Along the way, we prove a fairly general local existence theorem and an analogue of Peano's uniqueness theorem for measure differential equations.

Finally, we show that the general theory is applicable in the study of differential equations with impulses or dynamic equations on time scales.

Keywords

• Measure differential equations
• Extremal solution
• Lower solution
• Upper solution
• Equations with impulses
• Dynamic equations on time scales