Abstract
In this work we study the following singular, fractional critical problem
(P lambda) { (-Delta)(s)u = lambda/u(gamma) + u(q) in Omega;
u > 0 in Omega,
u = 0, in R-N\Omega,
where Omega subset of R-N(N >= 3) is a bounded domain with smooth boundary partial derivative Omega, N > 2s, 0 < s < 1, lambda > 0, 0 < gamma < 1 < q <= 2(s)* - 1 = N+2s/N-2s. Here (-Delta)(s) is the fractional Laplace operator defined as
(-Delta)(s)u(x) -1/2 integral(N)(R) u(x + y) + u(x-y) - 2u(x)/vertical bar y vertical bar(N+2s) dy, for all x is an element of R-N.
We use variational methods, in order to show the existence of multiple positive solutions to the problem (P-lambda) for different values of lambda.