Elliptic problems with a Hardy potential and critical growth in the gradient: Non-resonance and blow-up results

In this article we analyze existence and nonexistence of positive solutions to problem The main results are the following: (i) If the quadratic term in the gradient appears in the equation as a reaction term (− u2) and λ>0, then there is no solution to problem (P−) (even in a very weak sense). (ii) If the quadratic term in the gradient appears in the equation as an absorption term (+ u2), then there exists a positive solution to (P+) for all λ>0 and f L1(Ω).