On a singular nonlinear semilinear elliptic problem

where K(x)μC2,b(V9 ), a, pμ(0, 1) and l is a real parameter. Such singular elliptic problems arise in the contexts of chemical heterogeneous catalysts, nonNewtonian fluids and also the theory of heat conduction in electrically conducting materials, see [3, 5, 8, 9] for a detailed discussion. Obviously (1.1) cannot have a solution uμC2(V9 ) if K(x) is not vanishing near ∂V. However, under various appropriate assumptions on K(x), we will obtain classical solutions of (1.1) for l belonging to a certain range, and we will also obtain some uniqueness criteria. Here a classical solution is a solution u of (1.1) which belongs to C2(V)mC(V9 ) with u>0 in V. We also study the boundary behaviour of solutions of (1.1), and we will show that the solution u of (1.1) lies in a certain Hölder class. The special case when K(x) is negative and l=0 has been studied by several authors. The existence and uniqueness of the solution were established by Crandall, Rabinowitz and Tartar [6], Del Pino [7], Gomes [10] and Lazer and McKenna