Large solutions for a class of nonlinear elliptic equations with gradient terms

In this paper we prove the existence, in a suitable sense, of a large solution (a solution that blows-up at the boundary) for a class of nonlinear elliptic equations whose model is -Delta(p)u + u + u\Vu\ = f in Omega, p > 1, p - 1 < q <= p and f (x) is an element of L-1 (Omega). The main tool in order to prove it relies on approximating the problem with a more regular one, prove local (i.e. independent from the behavior on the boundary) a priori estimates and local compactness for truncations in W-1,W-p(Omega). Such scheme of the proof is also applied in order to prove the existence of a solution for equations of the type -Delta(p)u + u + u\del u\(q) = f in R-N, where f(x) is an element of L-loc(1), (R-N) without any condition at infinity. Moreover, the local summability of the solution depending on the local summability of the datum is studied.