Positive solutions for logistic type quasilinear elliptic equations on RN

In this paper, we consider positive solutions of the logistic type p-Laplacian equation -Delta(p)u = a(x)\u\(p-2)u - b(x)\u\(q-1)u, x epsilon R-N (N greater than or equal to 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. (C) 2003 Elsevier Inc. All rights reserved.