New Aspects on the Solvability of a Multidimensional Functional Integral Equation with Multivalued Feedback Control

Abstract

The current study demonstrates the existence of solutions to a multidimensional functional integral equation with multivalued feedback. We seek solutions for the multidimensional functional problem that is defined, continuous, and bounded on the semi-infinite interval. Our proof is based on the technique associated with measures of noncompactness by a given modulus of continuity in the space in BC(R+). Also, some sufficient conditions are investigated to demonstrate the asymptotic stability of the solutions to that multidimensional functional equation. Additionally, we give an example and some particular cases to illustrate our outcomes.

Keywords

• multidimensional integral equation
• existence results
• measure of noncompactness
• Darbo fixed-point theorem
• multivalued feedback control