# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Local and global solutions of well-posed integrated Cauchy problems

### Tom 187 / 2008

Studia Mathematica 187 (2008), 219-232 MSC: 47D62, 26A33. DOI: 10.4064/sm187-3-2

#### Streszczenie

We study the local well-posed integrated Cauchy problem $$v'(t)=Av(t)+{t^{\alpha }\over {\mit\Gamma} (\alpha+1 )} \, x,\ \quad v(0)=0, \ \quad t\in [0, \kappa),$$ with $\kappa>0$, $\alpha \ge 0$, and $x\in X$, where $X$ is a Banach space and $A$ a closed operator on $X$. We extend solutions increasing the regularity in $\alpha$. The global case $(\kappa=\infty)$ is also treated in detail. Growth of solutions is given in both cases.

#### Autorzy

• Pedro J. MianaDepartamento de Matemáticas
Instituto Universitario de Matemáticas y Aplicaciones