International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 30, Pages 1933-1941

Unilateral boundary value problems with jump discontinuities

Nikolaos Halidias

Department of Statistics and Actuarial Science, School of Sciences, University of the Aegean, Samos, Karlovasi 83200, Greece

Received 16 May 2001; Revised 24 September 2001

Copyright © 2003 Nikolaos Halidias. 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.


Using the critical point theory of Szulkin (1986), we study elliptic problems with unilateral boundary conditions and discontinuous nonlinearities. We do not use the method of upper and lower solutions. We prove two existence theorems: one when the right-hand side is nondecreasing and the other when it is nonincreasing.