This paper deals with the existence of the positive solutions of the semilinear elliptic Dirichlet problem Δu+λuq+up=0 on a ball where 0〈q〈1,p〉pc≡(N+2)/(N-2)(N〉2) and λ∈R . Under the condition N<6 or N〉6, p〈pN , we prove that there exists a unique constant λ0〉0 , such that for λ=λ0 , there exists a unique radial singular solution and infinitely many of solutions. |