Jingjing Liu, Qihu Zhang, Chunshan Zhao
Abstract:
In this article, we study the existence of positive solutions
for the p(x)-Laplacian Dirichlet problem
in a bounded domain
.
The singular nonlinearity term f is allowed to be either
, or
as
for each
.
Our main results generalize the results
in [15] from constant exponents to variable exponents. In particular,
we give the asymptotic behavior of solutions of a simpler equation which is
useful for finding supersolutions of differential equations with variable
exponents, which is of independent interest.
Submitted July 2, 2013. Published July 7, 2014.
Math Subject Classifications: 35J25, 35J65, 35J70.
Key Words: p(x)-Laplacian; singular nonlinear term; sub-supersolution method.
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Jingjing Liu College of Mathematics and Information Science Zhengzhou University of Light Industry Zhengzhou, Henan 450002, China email: jingjing830306@163.com | |
Qihu Zhang (corresponding author) College of Mathematics and Information Science Zhengzhou University of Light Industry Zhengzhou, Henan 450002, China email:zhangqihu@yahoo.com, zhangqh1999@yahoo.com.cn | |
Chunshan Zhao Department of Mathematical Sciences Georgia Southern University Statesboro, GA 30460, USA email: czhao@GeorgiaSouthern.edu |
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