全空间RN上非变分型奇异拟线性椭圆方程组大解的存在性

摘要

研究一类非变分型奇异拟线性椭圆方程组div(｜x｜-ap｜ ▽u｜P2 ▽u)=f(x)uαvγ,div(｜x｜-bq｜ ▽v ｜q-2 ▽v)=g(x)uδuβ,x∈RN,在全空间RN上正大解的存在性问题.其中:u(x),v(x)＞0,并且当｜x｜→+∞时,u(x),v(x)→+∞,这里0≤α ＜p-1,0≤β＜q-1,γ,δ＞0,0≤a＜(N-p)/p,0≤b＜(N-q)/q,且σ=(p--1-α)(q-1-β)-γδ＜0.通过精细地构造上下解的方法,在适当的条件下证明,本问题至少存在一组大解.%Consider a class of non-variational type singular quasilinear elliptic system:div(｜x ｜-ap ｜▽u ｜p-2 ▽u) =f(x)uαvγ,div(｜x｜-bq ｜▽v｜q-2 ▽v) =g(x)uδvβ,x ∈ RN,withu(x),v(x) ＞0,andu(x),v(x)→+∞as ｜ x｜→+∞,where0≤α ＜p-1,0≤β ＜q-1,y,δ ＞0,0≤a ＜ (N-p)/p,0≤b ＜ (N-q)/q,andσ =(p-1-α)(q-1-β)-yδ ＜0.Through the method constructing upper and lower solution,it is proved that,under appropriate conditions,there is at least one set of large solutions to this equation system.