EXISTENCE OF MULTIPLE SOLUTIONS FOR A FRACTIONAL p-LAPLACIAN SYSTEM WITH CONCAVE-CONVEX TERM

摘要

In this article, we study the existence of multiple solutions for the following system driven by a nonlocal integro-differential operator with zero Dirichlet boundary conditions{(-?)_p^su = a(x)|u|^(q-2) u +2α/α + βc(x)|u|^(α-2) u|v|~β, in ?,(-?)_p^sv = b(x)|v|^(q-2) v +2β/α + βc(x)|u|α|v|^(β-2) v, in ?,u = v = 0, in Rn?,(0.1) where Ω is a smooth bounded domain in Rn, n > ps with s ∈(0,1) fixed, a(x), b(x), c(x) ≥ 0 and a(x),b(x),c(x) ∈L∞(Ω), 1 1 satisfy p<α + β