兰州大学机构库 >数学与统计学院
非光滑型 Ricceri 变分原理在 p(x)-Laplacian 方程中的应用
Alternative TitleThe 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 AbstractIn 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
Document Type学位论文
Identifierhttps://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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