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We consider a Dirichlet problem driven by a (p(z), q(z))-Laplacian and a reaction involving the sum of a parametric singular term plus a superlinear perturbation. We prove a bifurcation-type result describing the changes in the set of positive solutions as the parameter λ > 0 varies. Also we show that for every admissible parameter the problem has a smallest positive solution and obtain the monotonicity and continuity properties of the minimal solution map. [ABSTRACT FROM AUTHOR]

In this paper we study the existence of a positive solution for a nonlinear Dirichlet problem driven by the p -Laplacian and a reaction which has the competing effects of a singular term and of a convection (gradient dependent) term. Using the "frozen" variable method and eventually the Leray-Schauder Alternative Theorem, we show that the problem has a positive smooth solution. We mention that on the gradient dependent perturbation x ↦ f (z , x , y) , we do not impose any bilateral growth condition. [ABSTRACT FROM AUTHOR]

We consider a nonlinear elliptic Dirichlet problem driven by the anisotropic (p, q)-Laplacian and with a reaction which is nonparametric and has the combined effects of a singular and of a superlinear terms. Using variational tools together with truncation and comparison techniques, we show that the problem has at least two positive smooth solutions. [ABSTRACT FROM AUTHOR]