An Existence Theorem of Solution for a Singular Third-order Two-point Boundary Value Problem

By constructing suitable Banach space, an existence theorem is established under a condition of linear growth for the third-order boundary value problem u″′（t）＋f（t,u（t）,u′（t））=0,0〈t〈1,u（0）=u′（0）=u′（1）=0, where the nonlinear term contains first and second derivatives of unknown function. In this theorem the nonlinear term f（t, u, v, w） may be singular at t = 0 and t = 1. The main ingredient is Leray-Schauder nonlinear alternative.

解决“运动电荷在有界匀强磁场中偏转轨迹”三部曲

'运动电荷在有界匀强磁场中偏转问题'是教学与高考的难点,学生不会解题的关键问题就是不会画轨迹。通过'假设圆心与半径已知来画出全图,再根据题意确定入射与出射两点,从而可以得出运动轨迹。