关于非齐次柯西问题的强解(英文)

On the Strong Solution of Inhomogeneous Cauchy Problem

利用自反Banach空间中弱紧算子的因子分解技巧,对于一类非齐次项具有连续Lipschitz扰动的柯西问题,当其齐次项算子生成强连续算子半群且具有紧豫解式限制时,证明了方程强解的存在性.

Using the technique of factoring weakly compact operators though reflexive Banach spaces, this note proves that a class of ordinary differential equations with Lipschitz continuous perturbations has a strong solution when the problem is governed by a closed operator with compact resolvent.