Uniqueness of positive radial solutions of [formula omitted] in [formula omitted], [formula omitted

Abstract

We study the uniqueness of radially symmetric ground states for the semilinear elliptic partial differential equation Δ u + f ( u ) = 0 in R N , N ≥ 2 . Assuming that F ( t ) = ∫ 0 t f ( s ) d s is negative in ( 0 , u 1 ) and positive in ( u 1 , u ̄ ) , we obtain the uniqueness of nonnegative solutions with u ( 0 ) = sup u ∈ ( 0 , u ̄ ) in the case where S ( u ) = u f ′ ( u ) / f ( u ) is monotonically decreasing in [ u 1 , u ̄ ) .