一类右侧Riemann-Liouville分数阶p-Laplacian问题极值解的存在性（英文）  

The existence of extremal solutions for fractional p-Laplacian problems with the right-handed Riemann-Liouville fractional derivative

作　　者：薛婷婷 樊小琳 徐加波 XUE Tingting;FAN Xiaolin;XU Jiabo(School of Public Education,Xinjiang Institute of Engineering,Urumqi 830000,Xinjiang,China;School of Mathematics,China University of Mining and Technology,Xuzhou 221116,Jiangsu,China)

机构地区：[1]新疆工程学院公共基础学院,新疆乌鲁木齐830000 [2]中国矿业大学数学学院,江苏徐州221116

出　　处：《上海师范大学学报（自然科学版）》2019年第3期280-291,共12页Journal of Shanghai Normal University(Natural Sciences)

基　　金：Tianshan Youth Technology Talents Training Program(2017Q032);Doctoral Starting Funds of Xinjiang Institute of Engineering(2016xgy351812);Education Department of Xinjiang Uygur Autonomous Region(2017jyt012006)

摘　　要：研究了一类右侧Riemann-Liouville分数阶p-Laplacian问题的可解性。应用单调迭代法、上下解方法及Banach不动点定理,得到了极值解的存在性和唯一性的充分条件,并推广了已有的结果。最后给出例子验证结果。In this paper we study the solvability of fractional p-Laplacian problems involving the righthanded Riemann-Liouville derivative. By applying monotone iterative technique, lower and upper solutions method and the Banach fixed point theorem, we obtain sufficient conditions for the existence and uniqueness of extremal solutions, and extend the existing results. Finally, we provide an examples to illustrate the results.

关 键 词：右侧Riemann-Liouville分数阶导数 P-LAPLACIAN算子 上下解方法 单调迭代法 极值解 

分 类 号：O175.8[理学—数学]