一类四阶周期边值问题解的存在性与唯一性

运用Leray-Schauder 不动点定理,讨论四阶周期边值问题{u⁽⁴⁾(t)=f(t,u(t), u'(t)), t∈［0,1］,u⁽ⁱ⁾(0)=u⁽ⁱ⁾(1), i=0,1,2,3解的存在性与唯一性,其中f:［0,1］×R²→R连续。在允许非线性项f(t,x,y)关于x、y超线性增长的不等式条件下,获得了该问题解的存在性与唯一性。

Existence and uniqueness of solutions for a class fourth-order periodic boundary value problems

By using Leray-Schauder fixed point theorem, this paper discusses the existence and uniqueness of solutions for the fourth-order periodic boundary value problem{u⁽4)(t)=f(t,u(t),u'(t)), t∈［0,1］,u⁽ⁱ⁾(0)=u⁽ⁱ⁾(1), i=0,1,2,3,where f:［0,1］×R²→R continuous. existence and uniqueness of solutions is obtained under the inequality conditions that allow the nonlinear term f(t,x,y) to grow superlinearly on x and y.