Existence and asymptotic behavior of positive solution to a quasilinear elliptic problem in RNRN

The main purpose of this paper is to obtain the existence result concerning the problem −Δpu=a(x)f(u)−Δpu=a(x)f(u) in RNRN where N>2N>2. The proofs of the main theorems are based on the results due to Diaz–Saà [J.I. Diaz, J.E. Saà, Existence et unicite de solutions positives pour certaines equations elliptiques quasilineaires, CRAS 305 Serie I (1987) 521–524].