The comprehensive study of differential equations

微分方程综合研究

基本信息

批准号：
62302004
负责人：
KUSANO Takasi
金额：
$ 9.28万
依托单位：
HIROSHIMA UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Co-operative Research (A)
财政年份：
1987
资助国家：
日本
起止时间：
1987 至 1988
项目状态：
已结题

项目摘要

The present research project covers both ordinary differential equations and partial differential equations. As a consequence of active, enthusiastic and energetic investigations by the members of the group of researchers, organized for this project, a great number of significant and important results have been obtained in various branches of differential equations as listed below:(1) qualitative theory of nonlinear ordinary differential equations in the real domain;(2) analytic theory of ordinary and partial differential equations in the complex domain;(3) fundamential existence-uniqueness theory for linear partial differential equations of hyperbolic, elliptic and parabolic types;(4) theory of pseudo-differential operators;(5) scattering theory for wave and elastic wave equations;(6) the problem of existence and qualitative behavior of positive solutions of nonlinear elliptic partial differential equations in unbounded domains;(7) global existence and asymptotic behavior of solutions for nonlinear partial differential equations (or systems) of parabolic and hyperbolic types;(8) various fundamental problems for nonlinear partial differential equations arising in fulid dynamics and other applied sciences, such as the Navier-Stokes equation and the Boltzmann equation.Praticular mention is made of the new results obtained by the head investigator regarding(i) oscillation theory of higher order functional differential equations of neutral type;(ii) existence of various types of positive entire solutions for second order quasilinear elliptic equations generalizing the equation of prescribed mean curvature; and(iii) classification of positive entire solutions of a class of semilinear elliptic equations of arbitrary order.

本研究项目涵盖了普通微分方程和部分微分方程。由于为该项目组织的一组研究人员的积极，热情和充满活力的调查，在差分方程的各个分支中获得了许多重要和重要的结果，如下所示：（1）实际上和偏见的理论在真实域中的非线性普通差分方程的定性理论；双波利，椭圆形和抛物性类型的部分微分方程；（4）伪差异操作员的理论；（5）波和弹性波方程的散射理论；（6）非线性椭圆形方程的非线性部分差异域的非线性偏微分方程的积极溶液的存在和定性行为的存在和定性的溶液的全球范围内序列的（7）隔离的依从性行为；抛物线和双曲线类型；（8）在Fulid动态和其他应用科学中产生的非线性偏微分方程的各种基本问题，例如Navier-Stokes方程和Boltzmann方程。主张是由头部研究人员获得的新的结果的新结果构成的（i）在（i）启发式型中性构成中的多种效能理论（II）中的多个中性构造的; II（i）II中的多种依赖性（II）; II（i）II的临床依赖性（II）。准线性椭圆方程概括了处方平均曲率的方程；（iii）分类任意顺序的一类半线性椭圆方程的阳性解决方案。