一类非线性算子方程解的存在唯一性及其应用

Existence and Uniqueness of Solutions for a Class of Nonlinear Operator Equations and its Applications

该文在更广泛的条件下,利用锥理论和Banach压缩映象原理证明了序Banach空间中一类非线性算子方程解的存在唯一性定理,并应用到Banach空间中二阶非线性混合型微分-积分方程初值问题,改进并推广了已有的一些结果.

By using the cone theory and the Banach contraction mapping principle, the existence and uniqueness theorem of solutions for a class of nonlinear operator equations in ordered Banach spaces are investigated in more general condition. As an application, an existence and uniqueness theorem of solutions for initial value problems of nonlinear second order integro-differential equations of mixed type in Banach spaces are given. The results presented here improve and generalize some known results.