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Existence of two positive solutions for a class of semilinear elliptic equations with singularity and critical exponent

Jia-Feng LiaoJiu LiuPeng ZhangChun-Lei Tang — 2016

Annales Polonici Mathematici

We study the following singular elliptic equation with critical exponent ⎧ - Δ u = Q ( x ) u 2 * - 1 + λ u - γ in Ω, ⎨u > 0 in Ω, ⎩u = 0 on ∂Ω, where Ω N (N≥3) is a smooth bounded domain, and λ > 0, γ ∈ (0,1) are real parameters. Under appropriate assumptions on Q, by the constrained minimizer and perturbation methods, we obtain two positive solutions for all λ > 0 small enough.

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