四阶两点边值问题的正解

The positive solution of fourth-order two point boundary value problem

微分方程边值问题的解的存在性是数学中一个古老而重要的问题,这类问题在物理等学科中有着广泛的应用。通过在函数空间中构造一个特殊的锥,利用锥中不动点指数,讨论了一类四阶两点边值问题正解的存在性,关于非线性项的条件有很大的改进。

The boundary problem of differential equation is an old and important problem, which has found wide application in physics and other areas. By using of the theory of the fixed point index in cone, The paper studies the existence of one positive solution of the fourth-order two point boundary value problem. Thus the condition about the nonlinearity could be improved.