摘要
LetΩbe 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,{(a+b[u]^(2)_(s))(-Δ)^(s)u=vp+h_(1)(x,u,v,▽u,▽v),x∈Ω,(-Δ)^(s)v=u^(q)+h_(2)(x,u,▽,▽u,▽v),x∈Q,u,v>0,x∈Ω,u=v=0,x∈RN\Ω.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).
基金
supported by National Natural Science Foundation of China (No.11761030)
Hubei Provincial Natural Science Foundation of China (No.2022CFC016)
Cultivation Project for High-Level Scientific Research Achievements of Hubei Minzu University (No.PY20002)。
