一类不连续三阶两点边值问题的变号解

Sign-changing solution of a class of discontinuous third-order two-point boundary value problems

考察了一类含有一、二阶导数的奇异三阶两点边值问题的变号解,其中非线性项为强Caratheodory函数.通过估计非线性项的高度函数的积分建立了一个新的存在定理.主要工具是Hammerstein积分方程及Shaud-er不动点定理.

The sign-changing solution is considered for a class of singular third-order two-point boundary value problems with first and second derivatives,where the nonlinear term is a strong Caratheodory function.By estimating integration of the height function of nonlinear term,a new existence theorem is established.The main tools are the Hammerstein integral equation and the Schauder fixed point theorem.