Strong stability results for solutions of elliptic equations with power-like lower order terms and measure data

Let u(n) be the sequence of solutions of -div(a(x, u(n), delu(n)))+u(n)(q-1) u(n) = f(n), in Omega, u(n) = 0 on deltaOmega, where Omega is a bounded set in R-N and f(n) is a sequence of functions which is strongly convergent to a function f in L-loc(1)(OmegaK), with K a compact in Omega of zero r-capacity, no assumptions are made on the sequence f. on the set K. We prove that if a has growth of order p-1 with respect to delu (p > 1), and if q > r(p-1)/(r -p), then u(n) converges to u, the solution of the same problem with datum f, thus extending to the nonlinear case a well-known result by H. Brezis. (C) 2002 Elsevier Science (USA).