Decaying positive solutions of quasilinear elliptic equations in exterior domains in R2

The existence of decaying, positive solutions of quasilinear elliptic equations of the form Δu+φ(x,u)+x·∇u/|x|2 = 0 is established in an exterior domain Ω ⊂ R2, under suitable smoothness and growth conditions. The main result is proved by means of a supersolution– subsolution method given by Noussair and Swanson. By using phase plane analysis of a system of Liénard type, a supersolution and a subsolution of the above equation are found out. An extension of the main result to more general case is also attempted. Finally, some examples are attached.  2002 Elsevier Science (USA). All rights reserved.