NEUMANN PROBLEMS OF A CLASS OF ELLIPTIC EQUATIONS WITH DOUBLY CRITICAL SOBOLEV EXPONENTS

摘要

This paper deals with the Neumann problem for a class of semilinear elliptic equations -△u + u =|u|2*- 2u + μ|u|q- 2u in Ω, u/r=|u|s*- 2u on Ω, where 2* = 2N/N- 2,s*=2(N- 1)/N-2, 1 ＜ q ＜ 2, N ≥ 3, μ＞ 0,γ denotes the unit outward normal to boundaryΩ. By variational method and dual fountain theorem, the existence of infinitely many solutions with negative energy is proved.