Nonlinear Elliptic Equations on Weighted Sobolev Space

The main objective of this work is to show the existence of solutions for quasilinear elliptic boundary value problem. In addition, we study compactness, directness of the solution set along with existence of smallest and biggest solutions in the set. The presence of dependence on the gradient and the Leray–Lions operator are the main novelties. We have used sub-supersolution technique in our work.