Finite energy solutions for nonlinear elliptic equations with competing gradient, singular and L1 terms

In this paper we deal with the following boundary value problem {-Delta(p)u + g(u)vertical bar del u vertical bar(p) = h(u)f in Omega, u >= 0 in Omega, u = 0 on partial derivative Omega, in a domain Omega subset of R-N (N >= 2), where 1 <= p < N, g is a positive and continuous function on [0, infinity), and his a continuous function on [0, infinity) (possibly blowing up at the origin). We show how the presence of regularizing terms h and g allows to prove existence of finite energy solutions for nonnegative data f only belonging to L-1(Omega). (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).