| 具有无流边界p(x)-Laplace方程解的存在性 |
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| 引用本文： | 刘越里,田玉柱,何万生.具有无流边界p(x)-Laplace方程解的存在性[J].四川理工学院学报(自然科学版),2011,24(3):281-282. |
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| 作者姓名： | 刘越里 田玉柱 何万生 |
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| 作者单位： | 天水师范学院数学与统计学院,甘肃天水,741001 |
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| 基金项目： | 甘肃省自然科学基金资助项目 |
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| 摘 要： | 利用山路引理和喷泉定理容易得到当p(x)-Laplace方程有|u|p(x)-2u项时,方程解的存在性和多解性;当方程没有|u|p(x)-2u时,问题变得比较困难,利用最小作用原理得到无流边界p(x)-Laplace方程解的存在性,其中无流边界指的是{u=c,x∈Ω;∫Ω|▽u|p(x)-2(u/η)ds=0.
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| 关 键 词： | 无流边界 p(x)-Laplace方程 最小作用原理 |
Existence of Solution of p(x) -Laplace Equation with No Flux Boundary |
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| LIU Yue-li,TIAN Yu-zhu,HE Wan-sheng.Existence of Solution of p(x) -Laplace Equation with No Flux Boundary[J].Journal of Sichuan University of Science & Engineering:Natural Science Editton,2011,24(3):281-282. |
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| Authors: | LIU Yue-li TIAN Yu-zhu HE Wan-sheng |
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| Institution: | (Department of Mathematics and Statistics,Tianshui Normal College,Tianshui 741001,China) |
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| Abstract: | When a term of |u|p(x)-2u is involved in p(x)-Laplace equation,it is easy to get the existence of solution and multiplicity of this equation using mountain pass theorem and fountain theorem.Otherwise,we apply the principle least action to obtain the existence of solution of p(x)-Laplace equation with no flux boundary,where no flux boundary is in the following:{u=c,x∈Ω;∫Ω|▽u|p(x)-2(u/η)ds=0. |
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| Keywords: | no flux boundary p(x)-Laplace equation principle of least action |
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