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  

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

作　　者：魏利[1] Agarwal Ravi P 

机构地区：[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 [3]Department of Mathematics,Faculty of Science,King Abdulaziz University

出　　处：《数学物理学报（A辑）》2015年第5期867-877,共11页Acta Mathematica Scientia

基　　金：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);河北经贸大学科学研究计划重点项目(2013KYZ01)资助

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-Laplaucian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.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.

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 

分 类 号：O177.91[理学—数学]