Fractional Schrödinger-Poisson-Kirchhoff type systems involving critical nonlinearities

The paper is concerned with existence, multiplicity and asymptotic behavior of nonnegative solutions for a fractional Schrödinger-Poisson-Kirchhoff type system. As a consequence, the results can be applied to the special case (a+b‖u‖2)[(−Δ)su+V(x)u]+ϕk(x)|u|p−2u=λh(x)|u|q−2u+|u|2s∗−2uinR3,(−Δ)tϕ=k(x)|u|pinR3,‖u‖=∫R3∫R3|u(x)−u(y)|2|x−y|3+2sdxdy+∫R3V(x)|u|2dx1∕2,where a,b≥0 are two numbers, with a+b>0, 10 is a parameter, s,t∈(0,1), (−Δ)s is the fractional Laplacian, k∈L63+2t−p(3−2s)(R3) may change sign, V:R3→[0,∞) is a potential function, 2s∗=6∕(3−2s) is the critical Sobolev exponent, 1