无穷区间上p-Laplacian积微分方程极值解的存在性  

Existence of extremal solutions for the p-Laplacian integro-differential equation on infinite intervals

作　　者：方玉萍 王颖 FANG Yuping WANG Ying(School of Mathematics and Statistics, Linyi University, Linyi 276000, Chin)

机构地区：[1]临沂大学数学与统计学院,山东临沂276000

出　　处：《中山大学学报（自然科学版）》2017年第5期41-50,共10页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金(11626125);山东省自然科学基金(ZR2016AP04);山东省高等学校科技计划项目(J16LI03);临沂大学博士科研启动基金(LYDX2016BS080);大学生创新创业项目(201610452168)

摘　　要：带有p-Laplacian算子的积微分方程在应用力学、天体物理和经典电学中有着广泛的应用。非线性微分方程边值问题是微分方程研究领域的一个重要分支。因此,p-Laplacian积微分方程边值问题的研究有着巨大的理论和实际意义。系统地研究无穷区间上,较为复杂边值条件下的一类p-Laplacian积微分方程。利用单调迭代方法,在适当的条件下,不仅得到了方程极值解的存在性,而且得到了方程解的迭代序列。最后,通过一个例子说明了结果的实用性。The integro-differential equation with p-laplacian operator is widely used in applied mechanics,astrophysics and classical electrology.The boundary value problem of nonlinear differential equations is an important branch of differential equations.Therefore,it is a great theoretical and practical significance to study the boundary value problems of p-Laplacian integro-differential equations.A class of pLaplacian integro-differential equations with complex boundary conditions on infinite interval is systematically studied.By using the monotone iterative technique,the existence of extremal solutions as well as iterative schemes under the suitable conditions is established.At last,an example is given to demonstrate the use of the main result.

关 键 词：P-LAPLACIAN算子 积微分方程 单调迭代方法 极值解 无穷区间 

分 类 号：O175.8[理学—数学]