In this paper, we consider the semilinear elliptic equation (*)(mu) -Delta u + u = u(p-1) + uf(x), u > 0, u is an element of H-1 (R(N)), N > 2. For p = 2N/(N - 2), we show that there exists a positive constant mu* > 0 such that (*)(mu) possesses at least one solution if mu is an element of (0, mu*) and no solutions if mu > mu*. Furthermore, (*)(mu) possesses a unique solution when mu = mu*, and at least two solutions when mu is an element of (0, mu*) and 2 < N < 6. For N greater than or equal to 6, under some monotonicity conditions on f ((1.6)) we show that there exist two constants 0 < mu** ...
