Positive solutions for logistic type quasilinear elliptic equations on <f>RN</f>

In this paper, we consider positive solutions of the logistic type <f>p</f>-Laplacian equation −Δpu=a(x)&z.sfnc;u&z.sfnc;p−2u−b(x)&z.sfnc;u&z.sfnc;q−1u, x∈RN (N&ges;2). We show that under rather general conditions on <f>a(x)</f> and <f>b(x)</f> for large <f>&z.sfnc;x&z.sfnc;</f>, the behavior of the positive solutions for large <f>&z.sfnc;x&z.sfnc;</f> 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. [Copyright &y& Elsevier]