一类三阶拟线性微分方程非极端解存在性

The Existence of Non-extreme Solution of a Type of Third-order Quasilinear Differential Equation

大多数的拟线性微分方程不能写出其解的表达式,所以对解的性质的研究就显得尤为重要.研究了一类三阶拟线性微分方程非极端解的存在性.其中利用函数的单调性、积分计算以及积分换元等微积分知识研究了非极端解存在的必要性,利用Schauder-Tychonoff不动点定理研究了非极端解存在的充分性,得到了非极端解存在的充分必要条件.所得结果拓展了前人的结果.

Most of the quasilinear differential equation cannot indicate the expression of its solution, so it is very important to study the properties of the solution. This paper is concerned with the existence of non - ex- treme soIution of one type third - order quasilinear differential equation. The necessity of the existence of non - extreme solution is studied by using the calculus. The sufficiency of the existence of non - extreme solution is studied by using the Schauder - Tychonoff fixed point theorem. This paper obtained a necessary and sufficient condition with non - extreme solution of the third - order quasilinear differential equation. The result comple- ments and extends previously known ones.