Infinitely many solutions for The Brezis-Nirenberg problem with nonlinear Choquard equations

摘要

In this paper, we consider the following Brezis-Nirenberg problem with the Choquard equations: @@@ {-Delta u = integral(Omega) |u(y)|(2)(alpha)|x - y|(N-a) dy|u|(2)(alpha)* a -2u +lambda u in Omega, @@@ u = 0 on partial derivative Omega, @@@ where alpha is an element of(N- 4, N), Omega is a bounded smooth domain in R-N(N= 7) and 2(alpha)*a= N+ a/N2 is the Hardy-Littlewood-Sobolev critical exponent. We show that, for each lambda > 0, this problem has infinitely many solutions by using truncation method.

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