The Brezis-Nirenberg Problem for Fractional p-Laplacian Systems in Unbounded Domains

In this article we consider the following fractional p-Laplacian system {(-Delta(p))(s) u = Q(u) (u, v) + H-u (u, v) in Omega, (-Delta(p))(s) v = Q(v) (u, v) + H-v (u, v) in Omega, u, v >= 0, u, v not equal 0, in Omega, u = v = 0 in R-N\Omega, where Omega subset of R-N is an unbounded strip like domain, s is an element of(0, 1), p > 1 and ps < N, p(s)* = Np/N-ps, Q, H are homogeneous functions of degrees p and p(s)*, respectively. By means of the fractional p-Poincare inequality in infinite cylindrical domains, we prove the existence of nontrivial weak solutions for the above system through variational techniques. The present work extends some known Brezis-Nirenberg type results to the fractional p-Laplacian on unbounded domains.