Positive solutions for logistic type quasilinear elliptic equations on RN

In this paper, we consider positive solutions of the logistic type p-Laplacian equation −Δpu = a(x)|u|p−2u − b(x)|u|q−1u, x ∈ RN (N 2). We show that under rather general conditions on a(x) and b(x) for large |x|, the behavior of the positive solutions for large |x| can be determined. This is then used to show that there is a unique positive solution. Our results improve the corresponding ones in J. London Math. Soc. (2) 64 (2001) 107–124 and J. Anal. Math., in press.  2003 Elsevier Inc. All rights reserved