Abstract
The purpose of this paper is to study the existence of mild
solutions to a class of second order nonlinear evolution equations of the form
\begin{equation*}
\begin{cases}
u''(t)+A(u'(t))+B(u(t))\ni f(t), &t\in(0,T),\\
u(0)=u_0, \quad u'(0)=g(u')
\end{cases}
\end{equation*}
where
$A\colon D(A)\subseteq X\rightarrow 2^{X}$ is an $m$-accretive operator
on a Banach space $X,$ $B: X\rightarrow X$ is a lipschitz mapping,
$g\colon C([0,T];X)\to X$ is a function and $f\in L^1(0,T,X)$.
We obtain sufficient conditions for this problem to have at least a mild solution.
Publisher
Uniwersytet Mikolaja Kopernika/Nicolaus Copernicus University