Skip to content


  • 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


© Giovanni Anello 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.