项目名称: 变分框架下的一类非局部的椭圆问题
项目编号: No.11301204
项目类型: 青年科学基金项目
立项/批准年度: 2014
项目学科: 数理科学和化学
项目作者: 王春花
作者单位: 华中师范大学
项目金额: 23万元
中文摘要: 本项目主要在变分框架下研究高维的Choquard方程的基态解的存在性、唯一性及非退化性和非局部的Schoringer-Newton方程组和非线性项为Hartree型的带电磁位势的Schrodinger方程在位势函数和非线性项满足不同条件时解的存在性以及解的性质,尤其是无穷多解和多峰解的存在性。主要方法是拟应用目前应用广泛的有限约化方法结合偏微分方程中的正则性理论和先验估计。这类问题具有广泛的物理意义。我们希望通过研究这类非局部的椭圆问题发展出非线性泛函分析中的新的方法和工具。
中文关键词: 非对称的;临界指标;非局部;约法方法;无穷多解
英文摘要: Under variational structure, the programme mainly wants to study the existence、uniqueness and non-degeneracy of the state solutions and properties of these solutions for the Choquard equation in high dimension space and the existence of solutions especially infinite solutions and multi-bump solutions for the Schrodinger-Newton systems and an electromagnetic Schrodinger equation with Hartree nonlinearities in nonlocal elliptic problems under some general conditions of potential function and nonlinearity. The main method is the finite reduction method widely used at present which needs to combine the theories of regurality and prior estimates. This kind of problems have comprehensive physical backgrounds. We wish to develop new methods and new tools in nonlinear functionali analysis by investigating this kind of nonlocal elliptic problems.
英文关键词: nonsymmetric;critical exponents;nonlocal;reduction method;infinitely many solutions