具积分边界条件的三阶微分方程解的存在性问题研究

Study on the Existence of Solutions for a Third Order Differential Equation with Integral Boundary Conditions

摘要: 本文采用构造分段函数的方法、不动点定理、上下解的方法研究了带积分边界条件的三阶微分方程解的存在性问题。我们给出了其格林函数，构造了一个合适的锥和算子，其中非线性项Z满足Nagumo条件，进而我们获得了解存在的充分条件。

Abstract: In this paper, we study the existence of solutions of the third order differential equations with integral boundary conditions by using the method of constructing piecewise functions, the fixed point theorem and the method of upper and lower solutions. We give its Green’s function, construct a suitable cone and operator, where the nonlinear term satisfies Nagumo condition, and then obtain sufficient conditions for understanding the existence.