Existence of Positive Solutions to a Fractional-Kirchhoff System

Let Ω be a bounded smooth domain in RN(N≥3).Assuming that 0 <s <1,1 <p,q≤(N+2s)/(N-2s)with(p,q)≠(N+2s/N-2s,N+2s/N-2s),and a,b> 0 are constants,we consider the existence results for positive solutions of a class of fractional elliptic system below,■Under some assumptions of hi(x,u,v,▽u,▽v)(i=1,2),we get a priori bounds of the positive solutions to the problem(1.1) by the blow-up methods and rescaling argument.Based on these estimates and degree theory,we establish the existence of positive solutions to problem(1.1).