| 二阶非线性椭圆型微分方程解的Sturm比较定理 |
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| 引用本文： | 庄容坤,贾保国,王其如. 二阶非线性椭圆型微分方程解的Sturm比较定理[J]. 数学学报, 2017, 60(6): 1037-1046 |
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| 作者姓名： | 庄容坤 贾保国 王其如 |
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| 作者单位： | 1. 惠州学院数学系 惠州 516007;2. 中山大学数学科学学院 广州 510275 |
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| 基金项目： | 国家自然科学基金（11501238,11271380,11671406）;广东省自然科学基金（2014A030313641,2016A030313119）及广东省教育厅重大项目（2014KZDXM070） |
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| 摘 要： | 本文通过对一类含阻尼项的椭圆型微分方程建立几个微分不等式,得到几个新的Sturm型比较定理,将经典的Sturm比较定理推广到含阻尼项椭圆型微分方程,并给出一些具体应用的例子.
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| 关 键 词： | 二阶 非线性椭圆型微分方程 微分不等式 Sturm型比较定理 振动性 |
Strum Comparison Theorem of Solutions for Second Order Nonlinear Elliptic Differential Equations |
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| Rong Kun ZHUANG,Bao Guo JIA,Qi Ru WANG. Strum Comparison Theorem of Solutions for Second Order Nonlinear Elliptic Differential Equations[J]. Acta Mathematica Sinica, 2017, 60(6): 1037-1046 |
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| Authors: | Rong Kun ZHUANG Bao Guo JIA Qi Ru WANG |
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| Affiliation: | 1. Department of Mathematics, Huizhou University, Huizhou 516007, P. R. China;2. School of Mathematical, Sun Yat-Sen University, Guangzhou 510275, P. R. China |
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| Abstract: | We first establish some differential inequalities and then some new Sturm type comparison theorems for the second order nonlinear damped elliptic differential equations are obtained by using them. Our results generalize some classicial Sturm Comparison Theorems. Some examples are presented to illustrate their applications. |
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| Keywords: | second order nonlinear elliptic differential equation differential inequality Sturm comparison theorem oscillation |
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