Stability for semilinear elliptic variational inequalities depending on the gradient

Multiplicity of Positive Solutions for an Obstacle Problem in ℝ

“…Related to this kind of problem, the reader may consult Jianfu ( [10], [11]), where the author uses variational methods, Le [13] in which is used subsolution-supersolution techniques, Chang [4] where it is considered an obstacle problem related to discontinuous nonlinearities and Rodrigues [19] who considers combination of the obstacle problem with nonlocal equations in a class of free boundary problems. For more recent references we may cite Matzeu & Servadei [16], in which the authors adapt for inequalities the iterative technique contained in de Figueiredo, Girardi & Matzeu [6] for elliptic equations, Matzeu & Servadei [17] where the stability of solutions obtained in [16] are analized. Other results may be found in Servadei & Valdinoci [22], Mancini & Musina [15], Servadei ([21], [20]), Magrone, Mugnai & Servadei [14].…”