The non-homogeneous Cauchy problem of semigroup of linear operators

Abstract

This paper presents the results of ω-order reversing partial contraction mapping generated by the non-homogeneous Cauchy problem. We investigated several concepts of solution for non-homogeneous Cauchy problem where an analysis was arrived out on the relationship between C' strong and respectively C₀-solution. We showed that Z is the infinitesimal generator of a C₀-semigroup of contractions. Finally, we obtained that the problem has a unique classical solution and f, a member of L¹(a,b; X) is continuous on (a,b).