| 带Neumann 边界条件的$p(x)$-Kirchhoff 型椭圆系统的研究 |
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| 引用本文： | 代国伟,李晓燕.带Neumann 边界条件的$p(x)$-Kirchhoff 型椭圆系统的研究[J].数学研究及应用,2013,33(4):443-450. |
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| 作者姓名： | 代国伟 李晓燕 |
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| 作者单位： | 西北师范大学数学系, 甘肃 兰州 730070;西北师范大学数学系, 甘肃 兰州 730070 |
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| 基金项目： | 国家自然科学基金 (Grant No.11261052). |
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| 摘 要： | 本文研究一类带Neumann 边界条件的~$p(x)$-Kirchhoff 型系统解的存在性. 借助于Ekeland变分原理和变指数Sobolev空间理论, 我们给出使得该问题存在解的合适条件.由于Poincar\'{e} 不等式在$W^{1,p(x)}(\Omega)$ 中不再成立, 我们将在$W^{1,p(x)}(\Omega)$ 的某个子空间中证明Poincar\'{e}-Wirtinger 不等式.
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| 关 键 词： | 变分法 椭圆系统 非局部 Neumann 边界条件. |
| 收稿时间： | 2/8/2012 12:00:00 AM |
| 修稿时间： | 9/4/2012 12:00:00 AM |
On Nonlocal Elliptic Systems of $p(x)$-Kirchhoff-Type under Neumann Boundary Condition |
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| Guowei DAI and Xiaoyan LI.On Nonlocal Elliptic Systems of $p(x)$-Kirchhoff-Type under Neumann Boundary Condition[J].Journal of Mathematical Research with Applications,2013,33(4):443-450. |
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| Authors: | Guowei DAI and Xiaoyan LI |
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| Institution: | Department of Mathematics, Northwest Normal University, Gansu 730070, P. R. China;Department of Mathematics, Northwest Normal University, Gansu 730070, P. R. China |
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| Abstract: | This paper is concerned with the existence of solutions to a class of $p(x)$-Kirchhoff-type systems under Neumann boundary condition. By Ekeland Variational Principle and the theory of the variable exponent Sobolev spaces, we establish conditions ensuring the existence of solutions for the problem. Since the Poincar\'{e}'s inequality does not hold in the space $W^{1,p(x)}(\Omega)$, we shall prove the Poincar\'{e}-Wirtinger's inequality in a subspace of $W^{1,p(x)}(\Omega)$. |
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| Keywords: | variational method elliptic systems nonlocal Neumann boundary |
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