数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (2): 419-428.doi: 10.1016/S0252-9602(18)30757-4

• 论文 • 上一篇    下一篇

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

宋慧娟1, 尹景学2, 王泽佳1   

  1. 1. College of Mathematics and Informational Science, Jiangxi Normal University, Nanchang 330022, China;
    2. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
  • 收稿日期:2016-05-25 修回日期:2017-12-10 出版日期:2018-04-25 发布日期:2018-04-25
  • 通讯作者: Zejia WANG E-mail:zejiawang@jxnu.edu.cn
  • 作者简介:Huijuan SONG,E-mail:songhj@jxnu.edu.cn;Jingxue YIN,E-mail:yjx@scnu.edu.cn
  • 基金资助:

    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, and the Natural Science Foundation of Jiangxi Province of China (20151BAB211003).

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

Huijuan SONG1, Jingxue YIN2, Zejia WANG1   

  1. 1. College of Mathematics and Informational Science, Jiangxi Normal University, Nanchang 330022, China;
    2. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
  • Received:2016-05-25 Revised:2017-12-10 Online:2018-04-25 Published:2018-04-25
  • Contact: Zejia WANG E-mail:zejiawang@jxnu.edu.cn
  • Supported by:

    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, and 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-2u)=d(x)|u|r-2u + Gu(x, u, v) in Ω,
-div(h2(x)|▽v|q-2v)=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.

关键词: Weighted (p,q)-Laplacian, small sources, multiplicity

Abstract:

In this article, we study the existence of infinitely many solutions to the degenerate quasilinear elliptic system
-div(h1(x)|▽u|p-2u)=d(x)|u|r-2u + Gu(x, u, v) in Ω,
-div(h2(x)|▽v|q-2v)=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.

Key words: Weighted (p,q)-Laplacian, small sources, multiplicity