On a class of weighted anisotropic $p$-Laplace equation with singular nonlinearity

Abstract

We consider a class of singular weighted anisotropic $p$-Laplace equations. We provide sufficient condition on the weight function that may vanish or blow up near the origin to ensure the existence of at least one weak solution in the purely singular case and at least two different weak solutions in the purturbed singular case.

20 pages, comments are welcome