Multi-Valued Variational Inequalities in Unbounded Domains

The main focus in this chapter is on multi-valued quasilinear elliptic variational inequalities of the form in all of ℝN as well as in the exterior domain Ω = ℝN ∖ B̅(0̅,1̅ ), where only for simplifying our presentation A: X → X∗ is given by the p-Laplacian, that is, A = − Δp, see Section 6.3. The study of elliptic equations in unbounded domains and even more the study of multi-valued quasilinear elliptic variational inequalities in unbounded domains causes a number of additional difficulties, and therefore cannot be considered as just a straightforward extension of the bounded domain problems. That is why the multi-valued lower order term ℱa is of the form ℱa= aℱ(u) with a: ℝN→ ℝ (resp. a: Ω → ℝ ) satisfying a certain decay property at infinity