Existence and asymptotic behavior of radially symmetric ground states of quasi-linear singular elliptic equations

Abstract

Existence and asymptotic behavior of entire positive solutions of a class of quasi-linear elliptic equation - div ( | ∇ u | p - 2 ∇ u ) = ρ ( x ) f ( u ) , x ∈ R N is obtained. Under several hypotheses on the ρ ( x ) and f ( r ) , we obtain the existence of positive entire solution. Asymptotic behavior is discussed by constructing an upper solution. The results of this paper is new and extend previously known results.