International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 30, Pages 1933-1941
doi:10.1155/S0161171203013279

Unilateral boundary value problems with jump discontinuities

Abstract

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.