CONSTRAINED SEMILINEAR ELLIPTIC SYSTEMS ON R-N

The existence of solutions u in H-1 (R-N, R-M) boolean AND H-loc(2) (R-N, R-M) of a coupled semilinear system of second order elliptic partial differential equations on R-N of the form P[u] = f(x,u,partial derivative u), x is an element of R-N, under pointwise constraints is considered. The problem is studied via the constructed suitable topological invariant, the so-called constrained topological degree, which allows to get the existence of solutions of abstract problems considered as L-2 -realizations of the approximating sequence of systems obtained by the truncation of the initial system to bounded subdomains. The key step of the proof consists in showing the relative H-1-compactness of the sequence of solutions to the truncated systems by the use of the so-called tail estimates. The constructions rely on the semigroup approach combined with topological methods, as well as invariance/viability techniques.