一类四阶两点边值问题解的存在性

The Existence for a Class of Fourth-Order Two-Point Boundary Value Problem

应用Leray-Schauder原理,研究四阶两点边值问题u(4)(t)=f(t,u(t),u″(t)),t∈(0,1)u′(0)=u′(1)=u(0)=u(1)=0解的存在性,在两参数非共振条件以及非线性项f满足至多线性增长性条件下给出了此类问题有解存在的最优充分条件,最后举例说明了所获结果.

By using Leray-Schauder theorem, the optimal sufficient conditions for the existence of the solution of the problem {u′（0）=u′（1）=u^m（0）=u^m（1）=0^u（4）（t）=f（t,u（t）,u^n（t））,t∈（0,1） are obtained. In the end, an example is presented to illustrate the application of the obtained result.