二阶非线性微分方程组三点边值问题解的存在性

利用上下解方法及Schauder不动点定理,证明了二阶非线性微分方程组三点边值问题:y″=f(t,y,z,y′,z′)z″=g(t,y,z,y′,z′)y(-1)=A,y(1)=B,z(0)=C0,z′(0)=C1,解的存在性,并由此得到四阶非线性微分方程三点边值问题解的存在性,一定程度上推广了前人的一些结果[2],[3].作为文章结果的应用,讨论了奇摄动四阶半线性三点边值问题,得到该问题解的存在性及解的渐近估计.

一类四阶非线性奇异椭圆方程有限元解的加权模估计

利用有限元方法研究了一类四阶奇异非线性椭圆方程.首先利用B anach不动点定理证明了相应变分问题弱解的存在唯一性;其次分别给出了不考虑数值积分影响时解的加权H2模误差估计、加权L2模误差估计.

具有非线性斜导数边界条件的二阶完全非线性椭圆方程的障碍问题

在自然结构条件下证明了具有非线性斜导数边界条件的二阶完全非线性随圆方程障碍问题Ｗ＾２，∞解的存在性，唯一性和正则性。抗议了Ｓ。Ｌｅｎｈａｒ，Ｐ。Ｌ。Ｌｉｏｎｓ和陈亚浙等人关于Ｄｉｒｉｃｈｌｅｔ边界条件的工作。

CALCULATION OF NONLINEAR FREE－SURFACE FLOWS RESULTING FROM LARGE￣AMPLITUDE FORCED OSCILLATION OF A TWO－DIMENSIONAL BODY

The BEM combined with the time- st6pping scheme has been applied to the numerical calculation of fully nonlinear free surface flows generated by large amplitude forced transverse oscillation of two-dimensional body. Particular attention is paid on the compatibility of free surface and body surface conditions at the intersection point, and moving radiation boundary is adopted. A new calculating formula of the exact force on the body is also presented.The results demonstrate some nonlinear phenomena and indicate the stability and correctness of the numerical simulation.