The purpose of this work is to study the following singular problem: (Pλ) −div(a(x,∇u)) = u−α + λuqinΩ;u > 0, inΩ;u = 0, inℝn∖Ω; where Ω ⊂ ℝN, N ≥ 2 be a bounded smooth domain, λ is a positive parameter, p ≥ 2 such that N ≥ p and 0 < α ≤ 1, p − 1 < q ≤ p∗− 1, where p∗ = Np N−p. We employ the Nehari manifold approach and the fibering maps in order to show the existence of Tq,α such that for all λ ∈ (0,Tq,α), problem (Pλ) has at least two solutions.

中文翻译：

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奇异拟线性椭圆方程的多重性结果

这项工作的目的是研究以下奇异问题： (磷λ) -div(一种(X,∇你)) = 你-α + λ你q在Ω;你 > 0, 在Ω;你 = 0, 在ℝn∖Ω; 在哪里Ω ⊂ ℝñ,ñ ≥ 2是一个有界平滑域，λ是一个正参数，p ≥ 2这样ñ ≥ p和0 < α ≤ 1,p - 1 < q ≤ p*- 1,在哪里p* = ñp ñ-p.我们采用 Nehari 流形方法和纤维图来显示存在吨q,α这样对于所有人λ ∈ (0,吨q,α)， 问题(磷λ)至少有两个解决方案。