数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (2): 419-428.doi: 10.1016/S0252-9602(18)30757-4
宋慧娟1, 尹景学2, 王泽佳1
Huijuan SONG1, Jingxue YIN2, Zejia WANG1
摘要:
In this article, we study the existence of infinitely many solutions to the degenerate quasilinear elliptic system
-div(h1(x)|▽u|p-2▽u)=d(x)|u|r-2u + Gu(x, u, v) in Ω,
-div(h2(x)|▽v|q-2▽v)=f(x)|v|s-2v + Gv(x, u, v) in Ω,
u=v=0 on ∂Ω,
where Ω is a bounded domain in RN with smooth boundary ∂Ω, N ≥ 2, 1< r < p < ∞, 1< s < q < ∞; h1(x) and h2(x) are allowed to have "essential" zeroes at some points in Ω; d(x)|u|r-2u and f(x)|v|s-2v are small sources with Gu(x,u, v), Gv(x, u, v) being their high-order perturbations with respect to (u, v) near the origin, respectively.