Existence of the Solution of an Implicit Integro-Differential Equation of Order One

Abstract

Abstract. In this study, we establish the existence of the solution of a class of first order implicit integro-di¤erential equation of type F ðt; ðKxÞðtÞ; xðtÞ; x 0 ðtÞÞ ¼ 0; where F : J Â R 3 ! R, K : CðJÞ ! CðJÞ defined as ðKxÞðtÞ ¼ Ð t 0 kðt; sÞxðsÞds, Ex A CðJÞ, using the concept of viscosity solution.