Existence of multiple positive solutions for −Δ u −μ( u /∣ x ∣ 2 )= u 2*−1 +σ f ( x )

In this paper, we consider the semilinear elliptic problem$$- \Delta u - \mu (u/\left| x \right|^{2} ) = u^{{2* - 1}} + \sigma f(x)\,u > 0,\,u \in H_{0}^{1} (\Omega )$$ where Ω⊂ℝ N ( N ⩾3) is a bounded smooth domain such that 0∈Ω, σ>0 is a real parameter, $$\mu < \overline{\mu } = (N - 2)^{2} /4$$ and f ( x ) is some given function in L ∞ (Ω) such that f ( x )⩾0, f ( x )≢0 in Ω. Some existence results of multiple solutions have been obtained by implicit function theorem, monotone iteration method and Mountain Pass Lemma. Copyright © 2002 John Wiley & Sons, Ltd.