EXISTENCE AND MULTIPLICITY OF POSITIVE RADIAL SOLUTIONS FOR SEMILINEAR ELLIPTIC-EQUATIONS IN ANNULAR DOMAINS

The existence and multiplicity of positive radial solutions of equation DELTA-u + f(u) = 0 is studied in annular domains in R(n), n greater-than-or-equal-to 2. It is proven that if f(0) greater-than-or-equal-to 0,f is somewhere negative in (0, infinity) and superlinear at infinity, then there is a large positive radial solutions on all annuli. If f(0) < 0 and satisfies certain conditions, then the equation has no solution if the annuli are too wide. Multiplicity results are also obtained when f has many humps with positive areas.