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  • Research Article
  • Open Access

An existence theorem for an implicit integral equation with discontinuous right-hand side

Journal of Inequalities and Applications20062006:71396

  • Received: 8 December 2004
  • Accepted: 22 March 2005
  • Published:


We establish a result concerning the existence of solutions for the following implicit integral equation: , where is not supposed continuous with respect to the second variable.


  • Integral Equation
  • Existence Theorem
  • Implicit Integral Equation


Authors’ Affiliations

Department of Mathematics, University of Messina, Sant' Agata, Messina, 98166, Italy


  1. Agarwal RP, Meehan M, O'Regan D: Nonlinear Integral Equations and Inclusions. NOVA, New York; 2001.MATHGoogle Scholar
  2. Anello G, Cubiotti P: Parametrization of Riemann-measurable selections for multifunctions of two variables with application to differential inclusions. Annales Polonici Mathematici 2004,83(2):179–187. 10.4064/ap83-2-8MATHMathSciNetView ArticleGoogle Scholar
  3. Bonanno G: Differential inclusions with nonconvex right hand side and applications to implicit integral and differential equations. Rendiconti Accademia Nazionale delle Scienze detta dei XL Memorie di Matematica e Applicazioni Serie V 1996,20(1):193–203.MATHMathSciNetGoogle Scholar
  4. Castaing C, Valadier M: Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics. Volume 580. Springer, Berlin; 1977:vii+278.View ArticleMATHGoogle Scholar
  5. Cubiotti P: Non-autonomous vector integral equations with discontinuous right-hand side. Commentationes Mathematicae Universitatis Carolinae 2001,42(2):319–329.MATHMathSciNetGoogle Scholar
  6. Hewitt E, Stromberg K: Real and Abstract Analysis. A Modern Treatment of the Theory of Functions of a Real Variable. Springer, New York; 1965:vii+476.MATHGoogle Scholar
  7. Himmelberg CJ: Measurable relations. Fundamenta Mathematicae 1975, 87: 53–72.MATHMathSciNetGoogle Scholar
  8. Ricceri B: Sur la semi-continuité inférieure de certaines multifonctions [On the lower semicontinuity of certain multifunctions]. Comptes Rendus de l'Académie des Séances. Série I Mathématique 1982,294(7):265–267.MATHMathSciNetGoogle Scholar
  9. Ricceri ON, Ricceri B: An existence theorem for inclusions of the typeand application to a multivalued boundary value problem. Applicable Analysis 1990,38(4):259–270. 10.1080/00036819008839966MATHMathSciNetView ArticleGoogle Scholar
  10. Villani A: On Lusin's condition for the inverse function. Rendiconti del Circolo Matematico di Palermo. Serie II 1984,33(3):331–335. 10.1007/BF02844496MATHMathSciNetView ArticleGoogle Scholar