MULTIPLICITY OF SOLUTIONS OF WEIGHTED(p, q)-LAPLACIAN WITH SMALL SOURCE  

作　　者：宋慧娟 尹景学 王泽佳 

机构地区：[1]College of Mathematics and Informational Science, Jiangxi Normal University [2]School of Mathematical Sciences, South China Normal University

出　　处：《Acta Mathematica Scientia》2018年第2期419-428,共10页数学物理学报（B辑英文版）

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 China;the Natural Science Foundation of Jiangxi Province of China(20151BAB211003)

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）｜△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.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.

关 键 词：Weighted （p q）-Laplacian small sources MULTIPLICITY 

分 类 号：O175.25[理学—数学]