˖ڍመڙጲ
http://www.paper.edu.cn
Multiplicity of Solutions of Weighted
(p, q)-Laplacian with
Small Sources
Huijuan Song
1∗
, Jingxue Yin
2
, Zejia Wang
3
1
Department of Mathematics, Jilin University, Changchun 130012
2
School of Mathematical Sciences, South China Normal University, Guangzhou 510631
3
College of Mathematics and Informational Science,
Jiangxi Normal University, Nanchang 330022
Abstract: In this paper we study the existence of infinitely many solutions to the degenerate
quasilinear elliptic system
−div(h
1
(x)|∇u|
p−2
∇u) = d(x)|u|
r−2
u + G
u
(x, u, v) in Ω,
−div(h
2
(x)|∇v|
q−2
∇v) = f (x)|v|
s−2
v + 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 < N, 1 < s < q < N,
h
1
(x), h
2
(x) are allowed to have “essential” zeroes at some points in Ω, d(x)|u|
r−2
u and f (x)|v|
s−2
v 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
1 Introduction
The purpose of this paper is to study the multiplicity of solutions for the system with small sources:
−div(h
1
(x)|∇u|
p−2
∇u) = d(x)|u|
r−2
u + G
u
(x, u, v) in Ω,
−div(h
2
(x)|∇v|
q−2
∇v) = f (x)|v|
s−2
v + G
v
(x, u, v) in Ω,
u = v = 0 on ∂Ω,
(1)
Huijuan Song (1985-), female, Ph. D. student, major research direction: nonlinear diffusion equations. Jingxue Yin (1956-), male, professor,
major research direction: nonlinear diffusion equations. Correspondence author: Zejia Wang (1979-), female, associate professor, major research
direction: nonlinear diffusion equations.
∗
Supported by the Graduate Innovation Fund of Jilin University (No. 20121031).
- 1 -
剩余12页未读，继续阅读
资源评论
