Skip to content


  • Research Article
  • Open Access

Infinitely Many Solutions for a Boundary Value Problem with Discontinuous Nonlinearities

Boundary Value Problems20092009:670675

  • Received: 16 October 2008
  • Accepted: 11 February 2009
  • Published:


The existence of infinitely many solutions for a Sturm-Liouville boundary value problem, under an appropriate oscillating behavior of the possibly discontinuous nonlinear term, is obtained. Several special cases and consequences are pointed out and some examples are presented. The technical approach is mainly based on a result of infinitely many critical points for locally Lipschitz functions.


  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation
  • Nonlinear Term

Publisher note

To access the full article, please see PDF.

Authors’ Affiliations

Mathematics Section, Department of Science for Engineering and Architecture, Engineering Faculty, University of Messina, 98166 Messina, Italy
PAU Department, Architecture Faculty, University of Reggio, Calabria, 89100, Reggio Calabria, Italy


© G. Bonanno and G.M. Bisci 2009

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.