一类拟线性第二边值问题的存在唯一性

The Existence and Uniqueness for a Class of Pseudoulinear Second Boundary Value Problem

本文在ｆ（ｔ，ｘ），ｆｘ（ｔ，ｘ），β（ｔ）连续，ｆｘ（ｔ，ｘ）≥－β（ｔ），β（ｔ）≤π２０＋α２４，β（ｔ）π２０＋α２４，π０为方程αｓｉｎｘ２＋ｘｃｏｓｘ２＝０的最小正根条件下，证明了第二边值问题．ｘ＂＝αｘ＋ｆ（ｔ，ｘ），ｘ（０）＝ａ，ｘ（１）＝ｂ对于任给实数α，ａ。

In this paper, we study a class of pseudoulinear second boundary value problem of x'=αx+f(t,x),x(0)=a,x(1)=b.We proved existence and uniqueness for the solution under the conditions that f(t,x),f x(t,x),β(t)are all continuous and f x(t,x)≥-β(t),β(t)≤π 2 0+α 24,β(t)π 2 0+α 24,where π 0 is the minimal positive root of the αsinx2+xcosx2=0.