On the structure of positive solutions for a class of quasilinear equations

This paper studies the existence, nonexistence and uniqueness of positive solutions for a class of quasilinear equations. We also analyze the behavior of this solutions with respect to two parameters $\kappa$ and $\lambda$ that appears in the equation. The proof of our main results relies on bifurcation techniques, the sub and supersolution method and a construction of an appropriate large solutions.