含有广义p-Laplacian算子的双曲型非线性微分方程的单调性方法

数学物理学报 ›› 2015, Vol. 35 ›› Issue (5): 867-877.

含有广义p-Laplacian算子的双曲型非线性微分方程的单调性方法

魏利¹, Agarwal Ravi P^2,3

1 河北经贸大学数学与统计学院石家庄 050061;
2 Department of Mathematics, Texas A & M University-Kingsville, Kingsville, TX 78363, USA;
3 Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

收稿日期:2014-06-23 修回日期:2015-03-06 出版日期:2015-10-25 发布日期:2015-10-25
作者简介:Agarwal Ravi P,diandianba@yahoo.com
基金资助:
国家自然科学基金(11071053)、河北省自然科学基金(2014207010)、河北省教育厅科学研究计划重点项目(ZH2012080)和河北经贸大学科学研究计划重点项目(2013KYZ01)资助

Monotonicity Method for Hyperbolic Type Nonlinear Differential Equation with Generalized p-Laplacian

Wei Li¹, Agarwal Ravi P^2,3

1 School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061;
2 Department of Mathematics, Texas A & M University-Kingsville, Kingsville, TX 78363, USA;
3 Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Received:2014-06-23 Revised:2015-03-06 Online:2015-10-25 Published:2015-10-25

摘要/Abstract

摘要：

利用伪单调算子和极大单调算子值域的扰动结果,得到了含有广义p-Laplacian算子、具混合边值条件的双曲型非线性微分方程存在唯一解的抽象结论,是对含有广义p-Laplacian算子的非线性椭圆方程和抛物方程相关研究工作的推广.运用了一些新的证明技巧.而且,展示了这个唯一解与某极大单调算子零点之间的关系.

关键词: 伪单调算子, p-Laplacian算子, 次微分, 双曲型非线性微分方程, 混合边界

Abstract:

By using the results on the perturbations of the ranges for pseudo-monotone operators and maximal monotone operators, we present the abstract result for the existence of the unique solution of hyperbolic type nonlinear differential equation involving the generalized p-Laplacian with mixed boundaries. It is an extension of the corresponding studies on nonlinear elliptic equation and nonlinear parabolic equation with generalized p-Laplacian. Some new techniques are employed in the discussion. Moreover, the connections between the unique solution studied in this paper and the zero point of a maximal monotone operator is exemplified.

Key words: Pseudo-monotone operator, p-Laplacian, Subdifferential, Hyperbolic type nonlinear differential equation, Mixed boundaries

中图分类号:

O177.91

魏利, Agarwal Ravi P. 含有广义p-Laplacian算子的双曲型非线性微分方程的单调性方法[J]. 数学物理学报, 2015, 35(5): 867-877.

Wei Li, Agarwal Ravi P. Monotonicity Method for Hyperbolic Type Nonlinear Differential Equation with Generalized p-Laplacian[J]. Acta mathematica scientia,Series A, 2015, 35(5): 867-877.

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