Well-posedness results for abstract generalized differential equations and measure functional differential equations

Abstract

In the first part of the paper, we consider nonlinear generalized ordinary differential equations whose solutions take values in infinite-dimensional Banach spaces, and prove new theorems concerning the existence of solutions and continuous dependence on initial values and parameters. In the second part, we apply these results in the study of nonlinear measure functional differential equations and impulsive functional differential equations with infinite delay.

Keywords

• Existence and uniqueness
• Continuous dependence
• Osgood theorem
• Differential equations in Banach spaces
• Functional differential equations
• Kurzweil integral