Nonhomogeneous singular problems with convection

We consider a nonlinear Dirichlet eigenvalue problem driven by a general nonhomogeneous differential operator and a reaction that exhibits the combined effects of a singular term and a convective perturbation. Using truncations and comparison techniques, and eventually the Leray–Schauder alternative principle (fixed point theory), we show that for all small values of the parameter \(\lambda >0\) $\lambda >0$ , the problem has a positive smooth solution.