一類Neumann邊界的Kirchhoff型方程無窮多解的存在性

趙仕海，索洪敏，雷春雨，張鵬

（1.貴州民族大學(xué)理學(xué)院，貴州貴陽550025；2.遵義師范學(xué)院，數(shù)學(xué)與計(jì)算科學(xué)學(xué)院貴州遵義563002）

一類Neumann邊界的Kirchhoff型方程無窮多解的存在性

趙仕海1，索洪敏1，雷春雨1，張鵬2

（1.貴州民族大學(xué)理學(xué)院，貴州貴陽550025；2.遵義師范學(xué)院，數(shù)學(xué)與計(jì)算科學(xué)學(xué)院貴州遵義563002）

利用臨界點(diǎn)理論中的定理，研究一類Neumann邊界的Kirchhoff型方程無窮多解的存在性，并獲得了一些新的可解性條件。

Kirchhoff型方程；臨界點(diǎn)；Neumann邊界；無窮多解；存在性

本文考慮如下的Kirchhoff方程：

1 預(yù)備知識(shí)

2 主要結(jié)果及其證明

由(?1)知I(u)是偶泛函，再由引理1和引理2，得到方程（1）存在無窮多解.定理1證畢.

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（責(zé)任編輯：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

貴州省科學(xué)技術(shù)基金資助項(xiàng)目（黔科合J字[2013]2141號(hào)，黔教科研發(fā)[2013]405號(hào)）

趙仕海，男（仡佬族），貴州石阡縣人，在讀碩士,主要從事非線性泛函分析研究。