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)|△u|q-2△v)=f(x)|v...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)|△u|q-2△v)=f(x)|v|s-2v+Gv(x,u,v) in Ω, u=v=0 on δΩ where Ω is a bounded domain in RN with smooth boundary δΩ, 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.展开更多
基金Supported by the National Natural Science Foundation of China(11426122,11371153,and 11361029)the Specialized Research Fund for the Doctoral Program of Higher Education of Chinathe Natural Science Foundation of Jiangxi Province of China(20151BAB211003)
文摘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)|△u|q-2△v)=f(x)|v|s-2v+Gv(x,u,v) in Ω, u=v=0 on δΩ where Ω is a bounded domain in RN with smooth boundary δΩ, 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.