| 关于一类带有非线性边界条件的拟线性椭圆方程 |
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| 引用本文： | 满守东,章国庆,刘三阳.关于一类带有非线性边界条件的拟线性椭圆方程[J].应用数学,2011,24(1). |
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| 作者姓名： | 满守东 章国庆 刘三阳 |
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| 作者单位： | 1. 上海理工大学理学院,上海,200093
2. 西安电子科技大学理学院,陕西西安,710071 |
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| 基金项目： | Supported by Shanghai Leading Academic Discipline Project (S30501) |
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| 摘 要： | 本文研究了一类带有非线性边界条件的拟线性椭圆方程.在比常用的经典条件弱的假设条件下,得到该方程所对应的能量泛函存在有界Palais-Smale序列.然后,利用山路引理,得到该方程非平凡解的存在性.最后,给出一个例子,说明所给的条件比经典条件弱.
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| 关 键 词： | 有界Palais-Smale序列 非线性边界条件 山路引理 非平凡解 |
On a Class of Quasilinear Elliptic Equations with Nonlinear Boundary Condition |
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| MAN Shoudong,ZHANG Guoqing,LIU Sanyang.On a Class of Quasilinear Elliptic Equations with Nonlinear Boundary Condition[J].Mathematica Applicata,2011,24(1). |
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| Authors: | MAN Shoudong ZHANG Guoqing LIU Sanyang |
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| Institution: | MAN Shoudong1,ZHANG Guoqing1,LIU Sanyang2(1.College of Science,University of Shanghai for Science and Technology,Shanghai 200093,China,2.Department of Applied Mathematics,Xidian University,Xi'an 710071,China) |
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| Abstract: | In this paper,we investigate a class of quasilinear elliptic equations with nonlinear boundary condition.The existence of bounded Palais-Smale sequences for the corresponding functional of the equation is obtained under hypotheses weaker than those commonly used in the literature.Then,by applying Mountain Pass Lemma,the existence of nontrivial solution is confirmed.Furthermore,we give an example which illustrates that the condition we give is more general than the superquadratic growth condition. |
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| Keywords: | Bounded Palais-Smale sequence Nonlinear boundary condition Mountain Pass Lemma Nontrivial solution |
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