Ground state solutions for singular p-Laplacian equation in [formula omitted

Abstract

In this work, we study the ground state solution for the class of singular quasilinear elliptic problem of the form − div ( | x | − a p | ∇ u | p − 2 ∇ u ) + h ( | x | ) | u | m − 2 u = H ( | x | ) | u | q − 2 u , x ∈ R N , where 1 < p < N , a < N − p p and h ( r ) , H ( r ) ⩾ 0 . We prove the compactly embedding results of the weighted Z = D a , r 1 , p ( R N ) ∩ L h , r m ( R N ) space of radially symmetric functions and then obtain the existence of nontrivial ground state solution.