一类Neumann边界的Kirchhoff型方程无穷多解的存在性

赵仕海，索洪敏，雷春雨，张鹏

（1.贵州民族大学理学院，贵州贵阳550025；2.遵义师范学院，数学与计算科学学院贵州遵义563002）

一类Neumann边界的Kirchhoff型方程无穷多解的存在性

赵仕海1，索洪敏1，雷春雨1，张鹏2

（1.贵州民族大学理学院，贵州贵阳550025；2.遵义师范学院，数学与计算科学学院贵州遵义563002）

利用临界点理论中的定理，研究一类Neumann边界的Kirchhoff型方程无穷多解的存在性，并获得了一些新的可解性条件。

Kirchhoff型方程；临界点；Neumann边界；无穷多解；存在性

本文考虑如下的Kirchhoff方程：

1 预备知识

2 主要结果及其证明

由(ƒ1)知I(u)是偶泛函，再由引理1和引理2，得到方程（1）存在无穷多解.定理1证毕.

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（责任编辑：朱 彬）

The Existence of Infinitely Many Solutions for a Class of Kirchhoff Equation with Neumann Boundary

ZHAO Shi-hai1，SUO Hong-min1，LEI Chun-yu1，ZHANG Peng2
(1.School of Science,Guizhou Minzu University,Guiyang 550025,China;2.Zunyi Normal College,Zunyi 563002,China)

By using the theorem in critical point theory,the existence of infinitely many solutions for a class of Kirchhoff equation involving Neumann boundary is studied.Besides,some new solvability conditions are obtained.

Kirchhoff equation;the critical point;Neumann boundary;infinitely many solutions;existence

O175.25

A

1009-3583（2016）-0111-03

2016-01-12

贵州省科学技术基金资助项目（黔科合J字[2013]2141号，黔教科研发[2013]405号）

赵仕海，男（仡佬族），贵州石阡县人，在读硕士,主要从事非线性泛函分析研究。