2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152329The existence of a solution, convergence and stability of the penalty method for variational inequalities with nonsmooth unbounded uniformly and properly monotone operators in Banach spase $B$ are investigated. All the objects of the inequality - the operator A, "the right-hand part" $f$ and the set of constrains $Ω$ - are to be perturbed. The stability theorems are formulated in terms of geometric characteristics of the spaces $B$ and $B^*$. The results of this paper are continuity and generalization of the Lions' ones, published earlier in \cite{l}. They are new even in Hilbert spaces.14 pages, LaTexFunctional Analysistext