The Existence, Uniqueness, and Measurability of a Stopped Semilinear Integral Equation

Abstract

In this article, we prove the existence, uniqueness, and measurability of the solution for the following stopped semimonotone nonlinear integral equation

We also improve the previous results under weaker assumptions.

Keywords:

• Existence and uniqueness
• Measurability
• Monotone nonlinearity
• Semilinear evolution equation
• Stopped integral equation

Mathematics Subject Classification:

• 60H15
• 35R60
• 35RXX

The authors would like to thank Professor S. Ladde and the referee for their careful reading of the manuscript and also their valuable comments.