Existence and asymptotic behavior of solutions of semilinear Cauchy problems with non dense domain via extrapolation spaces (Q1864678)

This work concerns the so-called abstract Cauchy problem (ACP), i.e., \(x'(t)=A x(t)+f(t)\), \(t\) real, where \(A\) is a Hille-Yosida operator with nondense domain. The authors prove the existence and uniqueness of bounded almost-periodic, asymptotic almost-periodic and Eberlein-weak periodic solutions to the ACP with nondense domain, provided that the nonhomogeneous term \(f(t)\) is a bounded almost-periodic, asymptotic almost-periodic, or Eberlein-weak periodic function. In order to do that, they make use of extrapolation spaces and extrapolation semi-group techniques. The paper concludes with an example, which illustrates the result.