一类半线性四阶弹性梁方程的解和正解

Solutions and Positive Solutions of a Class of Semilinear Fourth-Order Elastic Beam Equations

考察了一类含有所有导数的半线性四阶两点边值问题的解和正解的存在性．在力学中,这类边值问题描述了一端简单支撑,另一端被滑动夹子夹住的弹性梁的形变．结论表明,只要非线性项在其定义域的某个有界集上的“最大高度”是适当的,那么这类问题至少存在一个解或者正解．

The existence of the solutions and positive solutions is studied for a class of fourth-order two-point boundary value problems with all order derivatives. In the mechanics, the class of problems describes the deformations of the elastic beam, of which an end is simply supported and the other is clamped by sliding clamps. The results show that the class of problems has at least one solution or positive solution provided the ＂maximal height＂ of nonlinear term is appropriate on a bounded set of its domain.