| 非光滑型 Ricceri 变分原理在 p(x)-Laplacian 方程中的应用 |
| Alternative Title | The applications of nonsmooth version Ricceri's variational principle to the $p(x)$-Laplacian equation
|
| 代国伟 |
| Thesis Advisor | 范先令
|
| 2009-05-18
|
| Degree Grantor | 兰州大学
|
| Place of Conferral | 兰州
|
| Degree Name | 硕士
|
| Keyword | 变指数 Sobolev 空间
非光滑版 Ricceri 变分原理
非光滑版 Ricceri 变分原理
Neumann 边值问题
p(x)-Laplacian
|
| Abstract | 在这篇文章中，我们在有界域 \Omega 上分别考虑了包含 p(x)-Laplacian 算子的 Neumann 型的微分包含问题
\begin{equation}
\left\{
\begin{array}{l}
-\text{div}\left(\vert \nabla u\vert^{p(x)-2}\nabla
u\right)+\lambda(x)\vert u\vert^{p(x)-2}u\in \partial
F(x,u)+\partial G(x,u) \text{ in}
\,\,\Omega, \\
\frac{\partial u}{\partial \gamma }=0 \text{ \ on }\partial \Omega,%
\end{array}%
\right.\nonumber
\end{equation}
和 ~Dirichlet 型的微分包含问题
\begin{equation}
\left\{
\begin{array}{l}
-\text{div}\left(\vert \nabla u\vert^{p(x)-2}\nabla u\right)\in \partial F(x,u) \text{ in}
\,\,\Omega,\\
u=0 \quad \text{ on }\partial \Omega.
\end{array}
\right. \nonumber
\end{equation}
在对非线性项作适当假设后, 我们分别在变指数 ~Sobolev 空间
W^{1,p(x)}(\Omega) 和 W_0^{1,p(x)}(\Omega) 中, 利用非光滑型
Ricceri 变分原理得到了两类问题的无穷多解性. |
| Other Abstract | In this paper, we consider differential inclusion problem in a bounded domain $\Omega$ involving $p(x)$-Laplacian of Neumann-type
\begin{equation}
\left\{
\begin{array}{l}
-\text{div}\left(\vert \nabla u\vert^{p(x)-2}\nabla
u\right)+\lambda(x)\vert u\vert^{p(x)-2}u\in \partial
F(x,u)+\partial G(x,u) \text{ in}
\,\,\Omega, \\
\frac{\partial u}{\partial \gamma }=0 \text{ \ on }\partial \Omega,%
\end{array}%
\right.\nonumber
\end{equation}
and Dirichlet-type
\begin{equation}
\left\{
\begin{array}{l}
-\text{div}\left(\vert \nabla u\vert^{p(x)-2}\nabla u\right)\in \partial F(x,u) \text{ in}
\,\,\Omega,\\
u=0 \quad \text{ on }\partial \Omega.
\end{array}
\right. \nonumber
\end{equation}
With some suitable assumptions on nonlinearities, the existences of infinitely many solutions are obtained by using nonsmooth version Ricceri's variational principle in variable exponent Sobolev spaces W^{1,p(x)}(\Omega) and W_0^{1,p(x)}(\Omega), respectively. |
| URL | 查看原文
|
| Language | 中文
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| Document Type | 学位论文
|
| Identifier | https://ir.lzu.edu.cn/handle/262010/225476
|
| Collection | 数学与统计学院
|
Recommended Citation
GB/T 7714 |
代国伟. 非光滑型 Ricceri 变分原理在 p(x)-Laplacian 方程中的应用[D]. 兰州. 兰州大学,2009.
|
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