Existence results for a quasilinear elliptic problem with a gradient term via shooting method

The main purpose of our paper is to complete and improve a theorem of Dupaigne, Ghergu and Radulescu [Lane-Emden-Fowler equations with convection and singular potential, J. Math. Pures Appliquees (Journal de Liouville, 87(2007), 563-581).] showing the existence of solution for quasilinear elliptic equations where the nonlinearity depends on x, u and gradient term. The proofs combine O.D.E. techniques and shooting arguments. Previous developments require a monotonicity of the nonlinearity, while our main result is applied to a larger class of nonlinearities.