奇异分数阶Laplacian方程弱解存在唯一性的算子方法  

Operator method for the existence and uniqueness of weak solution to a fractional Laplacian equation with a singular nonlinearity

作　　者：王兴 彭达瑶 秦新强[1] 胡钢[1] WANG Xing;PENG Dayao;QIN Xinqiang;HU Gang(School of Science,Xi’an University of Technology,Xi’an 710054,China)

机构地区：[1]西安理工大学理学院,陕西西安710054

出　　处：《西安理工大学学报》2018年第3期299-303,共5页Journal of Xi'an University of Technology

基　　金：国家自然科学基金资助项目(11626185);陕西省科技厅科学研究计划资助项目(2017JQ1011)

摘　　要：本文研究一类带有奇异非线性项的分数阶Laplacian方程。由于奇异边值问题缺乏变分结构,所以临界点理论不再适用于弱解的存在性。本文首次建立了研究奇异分数阶Laplacian方程的算子方法,得到了正弱解存在唯一的一般性条件。并且该算子方法适用于其它一些奇异边值问题。This paper is devoted to the investigation of a class of fractional Laplacian equations with a singular nonlinearity.Since there is no variational structure for singular boundary value problems,the critical point theory could not be applied to obtain the existence of weak solution.This is the first time that operator method for fractional Laplacian equations involving a singular nonlinearity is established,with the general conditions of the existence and uniqueness of weak positive solution obtained.Moreover,the method is also useful for other singular boundary value problems.

关 键 词：算子方法 分数阶Laplacian 奇异非线性项. 

分 类 号：N55[自然科学总论]