具临界指数及奇异性的双调和方程解的存在性

文中考虑了下面带奇异项的双调和方程 {?²u-μ/|x|^αμ =λg(x)μ+k(x)|μ|^q-2μ+|μ|^2*-2μ,x∈Ω, μ∈D₀^2,2(Ω), x∈?Ω, 其中0∈Ω为R^N, N≥5中的有界区域, 0≤α, s < 4,2 < q < 2*(s) = 2(N-s)/N-4}, g(x), k(x) 为非负函数, 借助变分方法及嵌入映射D^2,2(R^N)→ L²*(R^N)的达到函数, 通过较精密的计算, 得到了上面方程解的存在性结果.

Existence of Solution for a |Singular Biharmonic Equation Involving Critical Exponent

In this paper, the authors present a result on existence to the following singular biharmonic equation involving singular terms {?²u-μ/|x|^α μ = λg(x)μ+k(x)|μ|^q-2 μ+|μ|^2*-2 μ,      x ∈ Ω,     μ ∈D₀^2,2(Ω),                                                        x ∈?Ω, where Ω is a bounded domain containing origin, Ω ( R^N, N ≥ 5, 0 ≤ α, s < 4,2 < q < 2^*(s) = 2(N-s)/N-4}, and g(x), k(x) are nonnegative functions, the existence of solution is shown by variational method, the acquired function for the imbedding mapping D^2,2(R^N) → L²*(R^N) plays an important role in the discussion.