Continuous selections of solution sets to Volterra integral inclusions in Banach spaces

Abstract

We consider a nonlinear Volterra integral equation governed by an m-accretive operator and a multivalued perturbation in a separable Banach. The existence of a continuous selection for the corresponding solution map is proved. The case when the m-accretive operator in the integral inclusion depends on time is also discussed.

Keywords

• Volterra integral equation
• m-accretive operator
• integral solution
• multivalued map.