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Unilateral boundary value problems with jump discontinuities. (English) Zbl 1109.35356

Summary: Using the critical point theory of Using a critical point theory of A. Szulkin [Ann. Inst. H. Poincaré, Anal. Non Linéaire 3, no. 2, 77–109 (1986; Zbl 0612.58011)], 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 another when it is nonincreasing.

MSC:

35J85 Unilateral problems; variational inequalities (elliptic type) (MSC2000)
35J60 Nonlinear elliptic equations
47J30 Variational methods involving nonlinear operators

Citations:

Zbl 0612.58011
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