中文摘要
该项目主要研究了五个方面的内容:微分方程的概周期解存在性和模包含问题;用不动点方法和变分方法研究二阶微分方程的周期解和同宿轨的存在性问题;时滞微分方程的分支问题和全局吸引子问题; 时滞微分方程的稳定性问题;反映扩散方程的行波解的存在性和单调性问题。解决了Gopalsamy and Liu猜测,回答了Seifert问题。
英文摘要
This project is mainly concerned with the following five contents: the existence of almost periodic solutions of differential equations and module containment; the periodic solutions and homoclinic solutions of second order differential equations via the fixed pointed theory and critical theory; the bifurcation and global attractor of delay differential equations; the stability problem of delay differential equations; the travelling wave and monotonicity of reaction-difffusion equation. We give an affirmative answer to Gopalsamy and Liu's conjecture and answer a problem due to Seifert.
结题摘要
该项目主要研究了五个方面的内容:微分方程的概周期解存在性和模包含问题;用不动点方法和变分方法研究二阶微分方程的周期解和同宿轨的存在性问题;时滞微分方程的分支问题和全局吸引子问题; 时滞微分方程的稳定性问题;反映扩散方程的行波解的存在性和单调性问题。解决了Gopalsamy and Liu猜测,回答了Seifert问题。
