Bifurcation of nonlinear elliptic equations on Smale's shrinking domains.

Smale 收缩域上非线性椭圆方程的分岔。

• 批准号: 2111769
• 金额: --
• 依托单位: University of Kent
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2018
• 资助国家: 英国
• 起止时间: 2018 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2111769
• 关键词: Bifurcation; nonlinear; elliptic; equations; Smale

Smale considered in the sixties boundary value problems for linear elliptic. Differential operators on manifolds and studied the existence of solutions when the underlying manifold is shrunk by a family of diffeomorphism. The supervisor of this project has taken up this idea and focussed on the existence of non-trivial solutions for nonlinear equations when shrinking a domain using bifurcation theory. By now this has only be done for Dirichlet boundary conditions on star-shaped domains in Euclidean space. The aim of this project is to obtain the existence of solutions of nonlinear PDEs when shrinking the domain for more general equations, more general boundary conditions and more general domains as in our previous work.

Smale在60年代考虑的线性椭圆边值问题。研究了流形上的微分算子，并研究了当其基础流形被一个复同态族收缩时解的存在性。这个项目的主管已经采取了这个想法，并集中在非线性方程的非平凡解的存在性时，收缩域使用分歧理论。到目前为止，这只对欧氏空间中星形域上的Dirichlet边界条件进行了研究。该项目的目的是像我们之前的工作一样，在缩小更一般的方程、更一般的边界条件和更一般的域时获得非线性偏微分方程解的存在性。