A Robin boundary problem with Hardy potential and critical nonlinearities

作者：Deng Yinbin^*; Jin Lingyu; Peng Shuangjie

来源：Journal d Analyse Mathematique, 2008, 104(1): 125-154.

DOI：10.1007/s11854-008-0019-3

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 nu denote the unit outward normal to partial derivative Omega. In this paper, we are concerned with the following class of boundary value problems:
(*) {-Delta u - mu u/|x|(2) + lambda u = |u|(2)*(-2)u + eta|u|(p-2)u, in Omega, partial derivative u/partial derivative v + alpha(x)u = 0, on partial derivative Omega,
where 2* = 2n/(n-2) is the limiting exponent for the embedding of H-1(Omega) into L-p(Omega), 2 < p < 2*, mu < <(mu)over bar> (Delta) double under bar (n-2)(2)/4, n >= 0 and lambda is an element of R-1 are parameters, and alpha(x) is an element of C(partial derivative Omega), alpha(x) >= 0. Through a compactness analysis of the functional corresponding to the problem (*), we obtain the existence of positive solutions for this problem under various assumptions on the parameters mu, lambda and the fact that 0 is an element of Omega or 0 is an element of partial derivative Omega.

• 出版日期2008-1
• 单位华中师范大学