Mathematical Sciences: Nonlinear Elliptic Boundary Value Problems

本课题将研究非线性椭圆型边值问题的可解性。主要将重点放在问题是半线性但线性部分的频谱未知，或者非线性部分干扰频谱的情况下。山路引理抽象的最新进展有望提供关于这些问题解的存在性和多解性问题的信息。要研究的问题是方程式中出现的基本问题，这些方程式对数学物理、生物数学和化学等领域的问题进行建模。

This project will study the solvability of nonlinear elliptic boundary value problems. Main emphasis will be placed in the cases where either the problem is semilinear but the spectrum of the linear part is not known, or the nonlinear part interferes with the spectrum. Recent developments on abstractions of the mountain pass lemma are expected to render information on the issue of existence and multiplicity of solutions for these problems. The problems to be studied are basic questions arising in equations that model problems in areas such as mathematical physics, biomathematics, and chemistry.