Existence and Bifurcation of the Positive Solutions for a Semilinear Equation with Critical Exponent

In this paper, we consider the semilinear elliptic equation[formula]Forp=2N/(N−2), we show that there exists a positive constantμ*>0 such that (*)μpossesses at least one solution ifμ (0, μ*) and no solutions ifμ>μ*. Furthermore, (*)μpossesses a unique solution whenμ=μ*, and at least two solutions whenμ (0, μ*) and 2