摘要
The existence of positive solutions of some semilinear elliptic equations of the form -Δu = kf(u) is studied. The major results are a nonexistence theorem which gives a λ* = λ*(f, Ω) > 0 below which no positive solutions exist and a lower bound theorem for u <sub>max</sub> for Ω a ball. As a corollary of the nonexistence theorem that describes the dependence of the number of solutions on λ, two other nonexistence theorems, and an existence theorem are also proved. 1980 Mathematics subject classification (Amer. Math. Soc.) (1985 Revision): 35 J 65,35 J 25. Keywords and phrases: positive solution, semilinear elliptic equation, degree theory. © 1991, Australian Mathematical Society. All rights reserved.