一类拟线性Kirchhoff型椭圆方程组多解的存在性

数学物理学报 ›› 2017, Vol. 37 ›› Issue (4): 671-683.

一类拟线性Kirchhoff型椭圆方程组多解的存在性

陈林

伊犁师范学院数学与统计分院新疆伊宁 835000

收稿日期:2016-12-07 修回日期:2017-05-24 出版日期:2017-08-26 发布日期:2017-08-26
作者简介:陈林,E-mail:clzj008@163.com
基金资助:
新疆高校科研计划重点资助项目（XJEDU2016I043）和伊犁师范学院科研计划项目（YSYB201519）

Multiple Solutions for a Quasilinear Elliptic System of Kirchhoff Type

Chen Lin

College of Mathematics and Statistics, Yili Normal University, Xinjiang Yining 835000

Received:2016-12-07 Revised:2017-05-24 Online:2017-08-26 Published:2017-08-26
Supported by:
Supported by the Key Scientific Research Project of Xinjiang Higher School Foundation (XJEDU2016I043) and the Scientific Research Project of Yili Normal University (YSYB201519)

摘要/Abstract

摘要：

该文运用Nehari流形和纤维环映射方法研究非局部拟线性椭圆方程组

非平凡弱解的存在性，其中Ω⊂R^N是一边界光滑的有界区域，△_pu=div（|▽u|^p-2▽u）是p-拉普拉斯算子，1 < p < N，α >1，β>1，α+β < p < p（k+1）< r < p^*（p^*=p^N/N-p若N>p，p^*=∞若N≤p），λ，μ >0，h（x），g₁（x），g₂（x）∈C（Ω）在Ω上可变号，M（s）=a+bs^k，a，b，k>0.

关键词: 拟线性椭圆方程组, Nehari流形, 纤维环映射, p-拉普拉斯算子

Abstract:

In this paper, using Nehari manifold and fibering maps we study the existence of multiple nontrivial nonnegative solutions for the nonlocal quasilinear elliptic system

where Ω is a bounded smooth domain of R^N, △_pu=div (|▽u|^p-2▽u) is the p-Laplacian with 1 < p < N,α >1,β>1,α+β < p < p (k+1) < r < p^*(p^*=p^N/N-p if N>p,p^*=∞ if N ≤ p),λ,μ >0,h (x),g₁(x),g₂(x)∈C (Ω) are functions which change sign in Ω and M (s)=a+bs^k,a,b,k>0.

Key words: Quasilinear elliptic system, Nehari manifold, Fibering map, p-Laplacian

中图分类号:

O175.2

陈林. 一类拟线性Kirchhoff型椭圆方程组多解的存在性[J]. 数学物理学报, 2017, 37(4): 671-683.

Chen Lin. Multiple Solutions for a Quasilinear Elliptic System of Kirchhoff Type[J]. Acta mathematica scientia,Series A, 2017, 37(4): 671-683.

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