On Some Noncoercive Variational Inequalities

Abstract

Let Ω be a bounded, connected, open C set of R . Let T be a nontrivial triangle with vertices x1, x2, and x3 and let T ⊂ Ω . We denote by Γ0 the side of the triangle with extremes x1 and x2, and by Γi , i = 1 2 , , the side with extremes xi and x3; we set int Γ0 = Γ0 1 2 – , { } x x and int Γi = Γi i x x – , { } 3 and assume that Γ0 2 2 0 ⊂ ∈ = { } , x R x and T x R x – , { } Γ0 2 2 0 ⊂ ∈ > . Furthermore, we consider an open set Ω0 0 ⊂ T , where T 0 is the topological interior of T, and the operators