ON POSITIVE SOLUTIONS OF SOME SEMILINEAR ELLIPTIC-EQUATIONS

The existence of positive solutions of some semilinear elliptic equations of the form -DELTA-u = lambda-f(u) is studied. The major results are a nonexistence theorem which gives a lambda* = lambda* (f, OMEGA) > 0 below which no positive solutions exist and a lower bound theorem for u(max) for OMEGA a ball. As a corollary of the nonexistence theorem that describes the dependence of the number of solutions on lambda, two other nonexistence theorems, and an existence theorem are also proved.