| 摘要: |
| 本文研究了一类分数阶 p(x)-Laplace 算子方程:
(-?p(x))^su = f(x, u), x ∈ Ω,
u=0, x∈R^N\Ω,
解的存在性和多解性问题. 在非线性项不满足 (AR) 条件时,
利用喷泉定理和分数变指数 Sobolev 空 间的相关理论, 得到方程无穷多解的存在性. |
| 关键词: 分数阶 p(x)-Laplace 方程 分数变指数 Sobolev 空间 喷泉定理 多解性 |
| DOI： |
| 分类号:35R11 ; 35J35 |
| 基金项目: |
|
| Multiplicity of solutions for a fractional p(x)-Laplacian equation |
|
张金国
|
|
Department of Mathematics, Jiangxi Normal University
|
| Abstract: |
| In this paper, we investigate the existence and multiplicity of solutions to a class
of fractional p(x)-Laplacian equation as follows:
(-?p(x))^su = f(x, u), x ∈ Ω,
u=0, x∈R^N\Ω,
By means of Fountain theorem and the theory of fractional variable exponent Sobolev space,
we show that the equation has a sequence of nontrivial solutions with high energies. |
| Key words: Fractional p(x)-Laplacian operator fractional variable exponent Sobolev space fountain theorem multiple solutions. |
