Banach空间二阶积-微分方程两点边值问题解的存在性

Existence of Solutions of Two-point Boundary Value Problem for Sencond-order Integro-differential Equations in Banach Spaces

利用上下解的单调迭代技巧讨论了Banach空间二阶积-微分方程两点边值问题-u″(t)=f(t,u(t),Su(t)),t∈I,u(0)=u(1)=θ解的存在性.其中f∈C(I×E×E,E),I=[0,1].在非线性项f满足一定的非紧性测度条件和单调性条件下,利用相应的线性方程解算子的谱半径,通过非紧性测度的精细计算,获得了其在上下解之间的最小、最大解的存在性以及在上下解之间解的唯一性.

This research uses a monotone iterative technique in the presence of lower and upper solutions to discuss the existence of solutions for two-point boundary value problem of sencond-order integro-differential equations in Banach space E -u （t） ：f（t,u（t） ,Su（t）） ,t∈ I,u（O） =u（1） =0, where f∈C（I×E×E,E） ,I=[0,1]. Under wide monotone conditions and the noncompactness measure condition of nonlinearity f, using the spectral radius of the solving operator for corresponding lin- ear equations and more accurate computation of measure of noncompactness, the existence of extremal solutions and unique so- lution between lower and upper solutions are obtained.