Banach空间非线性二阶微分积分方程组初值问题的解

Initial value problems for systems of nonlinear second-order integro-differential equations in Banach spaces

在一般的序Banach空间中研究了非线性二阶微分—积分方程组初值问题整体解的存在性。本文放宽了一般文中的上控制条件,将其中的非负常数M、N、L分别推广为有界可积非负函数M(t)、N(t)、L(t),同时函数f、g对第二个变量u由强增性减弱为M(t)-增,对第四个变量Tu由增性减弱为L(t)-增,通过一个新的比较结果和不动点定理,得到了非线性二阶微分—积分方程组初值问题的整体解,证明了整体解的存在性定理。

The existence of solutions of initial value problems for systems of nonlinear second-order integro-differential equations in Banach spaces is investigated. The nonnegative constants M, N, L in the upper dominant conditions are extended to the bounded integrable nonnegative functions M （t）, N （t）, L （t） and the stronger monotone increasing for the second variant u and the fourth variant Tu of the functions f, g is weaken to increase for M（t）-. L （t）-. Using a new comparison result and the fixed point theorem, the existence theorem of the solutions of initial value problems for systems of nonlinear second-order integro-differential equations is obtained.