非线性奇异三阶两点边值问题的一个正解存在定理

An Existence Theorem of Positive Solution for Nonlinear Singular Third-order Two-point Boundary Value Problems

研究了一类非线性三阶两点边值问题的正解.在这个问题中非线性项具有时间和状态的奇异性.通过构造适当的锥并且考察非线性项在无穷远处的增长速度的极限获得了一个正解存在定理.

This paper studies the positive solution of a class of nonlinear third-order two-point bound- ary value problems. In this problem, the nonlinearity may be singular with respect to both the time and space variables. By constructing suitable cone,the solvable set of the problem is given. Applying the solv- able set and the limit of growth rate of the nonlinearity at infinity,an existence theorem of positive solu- tion is obtained.