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

Source abstract

Abstract In this paper, we consider the semilinear elliptic problem where Ω⊂ℝ N ( N ⩾3) is a bounded smooth domain such that 0∈Ω, σ&gt;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 &amp; Sons, Ltd.