ARBITRARILY MANY SOLUTIONS FOR AN ELLIPTIC NEUMANN PROBLEM WITH SUB- OR SUPERCRITICAL NONLINEARITY

作者：Wang, Liping^*

来源：Communications on Pure and Applied Analysis, 2010, 9(3): 761-778.

DOI：10.3934/cpaa.2010.9.761

• Arbitrarily many solutions
• sub- or supercritical nonlinearity
• mean curvature

We consider the sub-ors upercritical Neumann elliptic problem -Delta u mu u = uN 2/N-2 epsilon, u > 0 in Omega; partial derivative u/partial derivative n = 0 partial derivative Omega, Omega being a smooth bounded domain in R-N, N >= 4, mu > 0 and epsilon not equal 0. Let H(x) denote the mean curvature at x. We show that for slightly sub- or supercritical problem, if epsilon min(x is an element of partial derivative Omega)H(x)> 0 then there always exist arbitrarily many solutions which blow up at the least curved part of the boundary as epsilon goes to zero.

• 出版日期2010-5
• 单位华东师范大学