分歧和一类p-Laplace问题的正解  

BIFURCATION AND POSITIVE SOLUTIONS OF A p-LAPLACIAN PROBLEM

作　　者：罗华 LUO Hua(School of Economics and Finance,Shanghai International Studies University,Shanghai 201620,China;School of Mathematics,Dongbei University of Finance and Economics,Dalian 116025,China)

机构地区：[1]上海外国语大学国际金融贸易学院,上海201620 [2]东北财经大学数学学院,辽宁大连116025

出　　处：《数学杂志》2020年第5期539-543,共5页Journal of Mathematics

基　　金：NSF of Liaoning Province(2019-MS-109);HSSF of Chinese Ministry of Education(20YJA790049).

摘　　要：本文研究一类在零点或无穷远点非渐近线性的p-Laplace问题.利用分歧和拓扑方法,获得了问题正解的存在性,不存在性和多解性结果,丰富和推广了正解存在性的已有结果.This paper studies a p-Laplacian problem with non-asymptotic nonlinearity at zero or infinity.By using the bifurcation and topological methods,the existence/nonexistence and multiplicity of positive solutions are obtained.The previous results of the existence of positive solutions are enriched and generalized.

关 键 词：分歧 正解 p-Laplace 拓扑方法 

分 类 号：O177.91[理学—数学] O175.2[理学—基础数学]