Kirchhoff方程解的存在性与多解性研究
发布时间：2018-08-27 13:40
【摘要】：Kirchhoff型方程是一种经典的非局部问题,近年来逐步引起人们的关注,相关研究日益深入。本文利用临界点理论讨论了两类带有参数Kirchhoff型非线性椭圆方程解的存在性,其中一类带有Dirichlet边界条件,而另一类带有非线性Neumann边界条件。对于第一类方程,主要利用变分原理研究了当参数变化时其解的存在性和多重性,建立了三个存在性结果,同时还讨论此类方程正解的分歧现象。对于第二类方程,主要利用Bonanno和Bisci变分原理研究其无穷多解的存在性,给出了保证存在无穷多解的若干条件。
[Abstract]:Kirchhoff equation is a kind of classical nonlocal problem, which has been paid more and more attention in recent years. In this paper, we discuss the existence of solutions for two classes of nonlinear elliptic equations with parameters Kirchhoff type by using the critical point theory, one with Dirichlet boundary conditions and the other with nonlinear Neumann boundary conditions. For the first kind of equations, the existence and multiplicity of the solutions are studied by means of variational principle, and three existence results are established. The bifurcation of positive solutions of this kind of equations is also discussed. For the second kind of equations, the existence of infinite solutions is studied by using Bonanno and Bisci variational principles, and some conditions are given to guarantee the existence of infinite solutions.
【学位授予单位】：湖南科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
本文编号：2207462
[Abstract]:Kirchhoff equation is a kind of classical nonlocal problem, which has been paid more and more attention in recent years. In this paper, we discuss the existence of solutions for two classes of nonlinear elliptic equations with parameters Kirchhoff type by using the critical point theory, one with Dirichlet boundary conditions and the other with nonlinear Neumann boundary conditions. For the first kind of equations, the existence and multiplicity of the solutions are studied by means of variational principle, and three existence results are established. The bifurcation of positive solutions of this kind of equations is also discussed. For the second kind of equations, the existence of infinite solutions is studied by using Bonanno and Bisci variational principles, and some conditions are given to guarantee the existence of infinite solutions.
【学位授予单位】：湖南科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
【参考文献】
相关期刊论文 前2条
1 张申贵;;一类Kirchhoff方程Neumann边值问题的可解性[J];宁夏师范学院学报;2015年06期
2 李健;杜泊船;赵昕;吕显瑞;;p-Kirchhoff型方程解的多重性[J];吉林大学学报(理学版);2013年04期
，本文编号：2207462
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