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

doi:10.1016/S0252-9602(18)30757-4

Acta mathematica scientia,Series B ›› 2018, Vol. 38 ›› Issue (2): 419-428.doi: 10.1016/S0252-9602(18)30757-4

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

Huijuan SONG¹, Jingxue YIN², Zejia WANG¹

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).

Abstract

Abstract:

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 + G_u(x, u, v) in Ω,
-div(h₂(x)|▽v|^q-2▽v)=f(x)|v|^s-2v + G_v(x, u, v) in Ω,
u=v=0 on ∂Ω,
where Ω is a bounded domain in R^N 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 G_u(x,u, v), G_v(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

Huijuan SONG, Jingxue YIN, Zejia WANG. MULTIPLICITY OF SOLUTIONS OF WEIGHTED (p, q)-LAPLACIAN WITH SMALL SOURCE[J].Acta mathematica scientia,Series B, 2018, 38(2): 419-428.

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

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