一类四阶两点边值问题的存在性与惟一性

Existence and uniqueness of solutions for fourth-order two-point boundary value problems

讨论四阶两点边值问题u(4)(x)=f(x,u(x)),x∈[0,1],u(0)=u(1)=u″(0)=u″(1)=0,其中f:[0,1]×R→R连续函数在不限制f(x,v)关于v的增长阶的情形下,用Leray-Schauder不动点定理得出其解存在性与惟一性.

The fourth-order two-point boundary value problem{u^（4）（x）=f（x,u（x））,x∈[0,1],u（0）=u（1）=u″（0）=u″（1）=0,discussed, where, f： [0, 1-] X R＂→R is continuous, in the general case without restrication for growth condition, the existence and uniqueness of solutions are obtained by Leray-Schauder fixed theorem.