Solutions to critical elliptic equations with multi-singular inverse square potentials
Solutions to critical elliptic equations with multi-singular inverse square potentials
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DOI：
10.1016/j.jde.2005.07.010
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发表时间：
2006-05
影响因子：
2.4
通讯作者：
D. Cao;P. Han
中科院分区：
文献类型：
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作者：
D. Cao;P. Han
设Ω是RN（N <$3）中的开有界区域，具有光滑边界<$Ω.我们研究多奇异临界椭圆问题，其中μi∈R，2*=2NN-2，ai∈Ω（1 i k），Q（x）是Ω '上的正有界函数。利用Moser迭代，证明了方程（*）在点ai（1 <$i <$k）处解的渐近性态.利用临界非线性系数的影响，我们用变分方法证明了问题（*）正解和变号解的存在性。
Let Ω be an open-bounded domain in RN(N⩾3) with smooth boundary ∂Ω. We are concerned with the multi-singular critical elliptic problem where μi∈R,2*=2NN-2,ai∈Ω(1⩽i⩽k) and Q(x) is a positive bounded function on Ω¯. Using Moser iteration, we prove the asymptotic behavior of solutions for (*) at points ai(1⩽i⩽k). By exploiting the effect of the coefficient of the critical nonlinearity, we, by means of a variational method, establish the existence of positive and sign-changing solutions for problem (*).