Boundary Value Problems
Volume 2009 (2009), Article ID 670675, 20 pages
Research Article

Infinitely Many Solutions for a Boundary Value Problem with Discontinuous Nonlinearities

1Mathematics Section, Department of Science for Engineering and Architecture, Engineering Faculty, University of Messina, 98166 Messina, Italy
2PAU Department, Architecture Faculty, University of Reggio, Calabria, 89100 Reggio Calabria, Italy

Received 16 October 2008; Accepted 11 February 2009

Academic Editor: Ivan T. Kiguradze

Copyright © 2009 Gabriele Bonanno and Giovanni Molica Bisci. 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.


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.