| 一类具有Robin边值条件的p-Laplace方程解的存在性 |
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| 引用本文： | 高娟娟,张争争,李解,苑言方,王富华.一类具有Robin边值条件的p-Laplace方程解的存在性[J].内江师范学院学报,2014(8):16-19. |
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| 作者姓名： | 高娟娟 张争争 李解 苑言方 王富华 |
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| 作者单位： | 河南科技大学数学与统计学院,河南洛阳471023 |
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| 基金项目： | 国家自然科学基金资助项目（51175150）,河南科技大学大学生研究训练计划（SRTP）. |
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| 摘 要： | 研究了一类具有Robin边值条件的p-Laplace方程解的存在性.利用Sobolev紧嵌入定理以及给定的假设条件证明了该类方程的能量泛函具有山路型结构并且满足（PS）条件,从而根据山路引理得到了该类方程在Sobolev空间W1,p（Ω）中非平凡弱解的存在性.
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| 关 键 词： | p-Laplace方程 Robin边值问题 紧嵌入定理 山路引理 |
Existence of Solutions for a Class of p-Laplace Equations Involving Robin Boundary Value Conditions |
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| GAO Juan-juan,ZHANG Zheng-zheng,LI Jie,YUAN Yan-fang,WANG Fu-hua.Existence of Solutions for a Class of p-Laplace Equations Involving Robin Boundary Value Conditions[J].Journal of Neijiang Teachers College,2014(8):16-19. |
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| Authors: | GAO Juan-juan ZHANG Zheng-zheng LI Jie YUAN Yan-fang WANG Fu-hua |
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| Institution: | (School of Mathematics and Statistics, He＇nan University of Science and Technology, Luoyang, He＇ nan 471023, China) |
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| Abstract: | A probe is made into the existence of a class of p-Laplace equations with Robin boundary value condition.By applying the Sobolev compact embedding theorem and assumptions given,it is proven that the energy functional of this type of equations is of a Mountain Pass type structure and satisfies the （PS）condition.Consequently,the existence of the nontrivial weak solutions of the p-Laplace equations in the Sobolev spaceW1,p（Ω）is obtained by the use of the Mountain Pass Lemma. |
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| Keywords: | p-Laplacian problems Robin boundary value problems compact embedding theorems mountain pass lemma |
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