一类具有高阶转向点的二次问题的奇摄动

Singular Perturbation of Quadratic Problem with Higher-order Turning Point

研究带有高阶转向点的二阶非线性微分方程的边值问题εy″=f(t)y′2+g(t,y)y(a,ε)=A,y(b,ε)=B的奇异摄动现象.在一定的条件下,得到了摄动解关于退化解的渐近性质及误差估计.

We consider the singular perturbation of the boundary value problem for second order quadriaticcally nonlinear differential equationswhen εy″=f(t)y′~2+g(t,y)y(a,ε)=A, y(b,ε)=BWhere it have truning point. Under appropriate conditions, we get the asymptotic behavior and error estimate.