带凹凸非线性Kadomtsev-Petviashvili方程解的存在性  

The Existence of Solutions to the Kadomtsev-Petviashvili Equation with Concave-convex Nonlinearity

作　　者：陈佼苹 林美琳 CHEN Jiaoping;LIN Meilin(College of Mathematics and Statistics,Fujian Normal University,Fuzhou Fujian 350117,China;School of Mathematics and Finance,Putian University,Putian Fujian 351100,China)

机构地区：[1]福建师范大学数学与统计学院,福建福州350117 [2]莆田学院数学与金融学院,福建莆田351100

出　　处：《莆田学院学报》2023年第5期23-26,共4页Journal of putian University

基　　金：国家自然科学基金资助项目(11971253)。

摘　　要：简要介绍Kadomtsev-Petviashvili方程解的研究现状,运用变分方法研究带凹凸非线性Kadomtsev-Petviashvili方程解的存在性。借助Nehari流形可以得到在R^(N)中,方程至少有一个非平凡解。This paper briefly introduces the research status of solutions to Kadomtsev-Petviashvili equation,and studies the existence of solutions of Kadomtsev-Petviashvili equation with concave-convex nonlinearity by using variational method.With the help of Nehari manifold,it can be obtained that the equation has at least one nontrivial solution in R^(N).

关 键 词：NEHARI流形 各向异性Sobolev嵌入 变分方法 KADOMTSEV-PETVIASHVILI方程 

分 类 号：O175.2[理学—数学]