Comparison principle for elliptic equations in divergence with singular lower order terms having natural growth

© World Scientific Publishing Europe Ltd.In this paper, we are concerned with the zero Dirichlet boundary value problem associated to the quasilinear elliptic equation -div(a(u)M(x)¿u) + H(x, u,¿u) = f(x), x ¿ ¿, where O is an open and bounded set in RN (N = 3), a is a continuously differentiable real function in (0,+8), M(x) is an elliptic, bounded and symmetric matrix, H(x,, ¿) is non-negative and may be singular at zero and f ¿ L1(¿). We give sufficient conditions on H, M and a in order to have a comparison principle and, as a consequence, uniqueness of positive solutions being continuous up to the boundary.