A SPECIAL HEMIVARIATIONAL INEQUALITY
Endre Buzog, Ildikó I. Mezei · 2003
Let X be a Banach space, X its dual and let T : X ! L p ( ,R k ) be a linear, continuous operator, where p, k 1, being a bounded open set in R N. Let K be a subset of X, A : K X , F : K K be set-valued mappings with nonempty values and j : ◊ R k ! R a Caratheodory function, which is locally Lipschitz in the second argument. Under some condition we guarantee solution for the following problem: find u 2 F(u) such that, for every v 2 F(u), (A(u),v u) + Z j 0(x,Tu(x),Tv(x) Tu(x))dx 0.