期刊论文

Kou, Bing-yu

英文

应用数学学报：英文版

0168-9673

2009

25

4

631-646

10.1007/s10255-008-8818-y

Manuscript received February 9, 2009. Supported by the National Natural Science Foundation of China (No. 10631030), the Program for New Century Excellent Talents in University (No.07-0350) and the Key Project of Chinese Ministry of Education (No.107081).

本校为第一且通讯机构

Let Omega be a bounded domain with a smooth C(2) boundary in R(N)(N >= 3), 0 is an element of (Omega) over bar, and n denote the unit outward normal to partial derivative Omega. We are concerned with the Neumann boundary problems: -div(vertical bar x vertical bar(alpha)vertical bar del u vertical bar(p-2)del u) = vertical bar x vertical bar(beta)u(p(alpha,beta)-1) - lambda vertical bar x vertical bar(gamma)u(p-1), u(x) > 0, x is an element of Omega, partial derivative u/partial derivative n = 0 on partial derivative Omega, where 1 < p < N and alpha < 0, beta < 0 such that p(alpha, beta) (sic) ...

让 &#937; 是有在 &#8477; N (N &#8805; 的一条光滑的 C 2 边界的一个围住的领域3 ) ， 0 &#8712; ，并且 n 表示对 &#8706;&#937; 向外正常的单位。我们涉及 Neumann 边界问题：&#8722;div (|x|&#945; |&#8711;u| p&#8722;2 &#8711;u)=|x|&#946; u p (&#945; ， &#946; )&#8722;1 &#8722; &#955;|x&#946;&#947; u p&#8722;1 , u (x)】 0， x &#8712; &#937; ， &#8706;u/&#8706;n = 0 在 &#8706;&#937; 上 1 【 p 【 N 和 &#945; 【 0， &#946; 【 0 以便 】 p， &#947; 】 &#945;&#8722;p。为各种各样的参数 &#945; ， &#946; 或 &#947; ，我们在情况中建立解决方案的某些存在结果 0 &#8712;...