一类四阶非线性边值问题的解和正解

Solution and Positive Solution to a Class of Nonlinear Fourth-order Boundary Value Problems

利用Schauder不动点定理及积分方程组技巧研究了一类四阶非线性边值问题的解和正解的存在性.在材料力学中,这类边值问题通常描述了一端简单支撑,另一端被活动夹子夹住的弹性梁的平衡状态.结论表明只要非线性项在其定义域的某个有界子集上的"最大高度"是适当的,该问题至少存在一个解或者正解.

The existence of solution and positive solution is studied for a class of fourth-order nonlinear boundary value problems by using Schauder fixed point theorem and the technique of system of integral equations.In the mechanics of material,the class of problems usually describes the equilibrium state of the elastic beam in which an end is simply supported and other end is Clamped by sliding clamps.The main results show that the problem has at least one solution or positive solution provided the 'maximal height' of nonlinear term on a bounded set of its domain.