精品文档---下载后可任意编辑中立型积分微分系统非局部问题解的存在性的开题报告原题目：On the Existence of Solutions for Nonlocal Problems in Neutral Type Integral-Differential Systems摘要：本文讨论中立型积分微分系统中的非局部问题解的存在性问题。我们考虑了一类具有时滞和非局部积分条件的积分微分系统，并证明了其解的存在性。该问题的关键在于构造了一个双线性算子，并且通过利用凸分析和 Banach 空间的合适性质，证明了该算子是有界的。进一步地，我们证明了该算子的预解有一个单独的解，这也导致了该问题解的唯一性。最后，我们给出了一些数值例子以验证所得结论的有效性。关键词：中立型积分微分系统；非局部问题；双线性算子；凸分析；唯一性Abstract: In this paper, we investigate the existence of solutions for nonlocal problems in neutral type integral-differential systems. We consider a class of integral-differential systems with delay and nonlocal integral conditions, and prove the existence of their solutions. The key to our problem is to construct a bilinear operator and prove its boundedness by using convex analysis and appropriate properties of Banach spaces. Moreover, we prove that the operator has a unique solution for its pre-solution, which also leads to the uniqueness of the solution to the problem. Finally, we give some numerical examples to validate the effectiveness of our results.Keywords: Neutral type integral-differential systems; Nonlocal problem; Bilinear operator; Convex analysis; Uniqueness
