m次积分半群和相应柯西问题的强解

m-times integrated semigroups and the strong solution of abstract cauchy problem

研究主算子为m次积分半群的无穷小生成元的一类线性非齐次发展方程强解存在的两个充要条件及判定强解存在的充分条件。最后 ,给出一个实例来验证本文的抽象结果。

In this paper, we introduce the strong solution of lnear differential equation whose principal operator is the infinitesimal generator of an m-times integrated semigroup and give two sufficient necessary conditions and a judgeing theorem. Then, we give an example to illustrate ourresults.