Existence of positive solutions for a class of degenerate or singular equations

Abstract

In this paper, we consider the class of equations − div ( | x | − 2 a ∇ u ) = A | x | 2 ( α + a ) u + u θ | x | b p , x ∈ R n ∖ { 0 } . where a , b ∈ R , n > 2 , A ∈ R , α > 0 and θ > 0 , p = 2 n n − 2 ( 1 + a − b ) . In various range of the parameters involved, we obtain both results of existence and nonexistence of positive solutions by combining the Mountain Pass Lemma and the Pohozaev-type identity.