一类Kirchhoff型问题无穷多解的存在性  

Existence of Infinitely Many Solutions for a Class of Kirchhoff-Type Problems

作　　者：叶红艳 索洪敏 安育成 YE Hongyan;SUO Hongmin;AN Yucheng(College of Data Science and Information Engineering,Guizhou Minzu University,Guiyang 550025,China;College of Science,Guizhou University of Engineering Science,Bijie 551700,China)

机构地区：[1]贵州民族大学数据科学与信息工程学院,贵阳550025 [2]贵州工程应用技术学院理学院,毕节551700

出　　处：《应用泛函分析学报》2019年第3期260-267,共8页Acta Analysis Functionalis Applicata

基　　金：国家自然科学基金(11661021,11861021);贵州民族大学科研基金(2017YB081)

摘　　要：本文应用变分方法和截断技巧研究一类具有Neumann边值条件的Kirchhoff型方程.首先,通过方程对应的能量泛函及解的定义获得平凡解的等价条件;其次,对非线性项进行了奇假设证明了紧致性条件;最后,立足于空间分解来获得该问题存在无穷多解,并且它们对应的能量泛函收敛到零.In this paper,we use a variational method and a truncation technique to study a class of Kirchhoff-type equations for Neumann boundary value problems.Firstly,the equivalence condition of trivial solutions is obtained by the definition of energy functionals and solutions corresponding to the equations;Secondly,the condition of compactness is proved by the odd hypothesis of the nonlinear term;Finally,the existence of infinite solutions is obtained based on spatial decomposition,and the corresponding energy functionals have zero gradation.

关 键 词：变分方法 Kirchhoff型方程 NEUMANN边值 截断技巧 无穷多解 

分 类 号：O177.91[理学—数学]