Boundary Value Problems
Volume 2009 (2009), Article ID 670675, 20 pages
doi:10.1155/2009/670675
Infinitely many solutions for a boundary value problem with discontinuous nonlinearities
Gabriele Bonanno1
and Giovanni Molica Bisci2
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
Abstract
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.