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<NN⩾6, under some monotonicity conditions onf((1.6)) we show that there exist two constants 0<μ**⩽μ**<μ* such that problem (∗)μpossesses a unique solution forμ∈(0, μ**), and at least two solutions ifμ∈(μ**, μ*).
& Li, Y.
(1996). Existence and Bifurcation of the Positive Solutions for a Semilinear Equation with Critical Exponent. Journal of Differential Equations, 130 (1), 179-200.