Inhomogeneous Gevrey ultradistributions and Cauchy problem

Inhomogeneous Gevrey Ultradistributions and Cauchy Problem

AMS Mathematics Subject Classification (2000): 46F05, 35E15, 35S05.

Inhomogeneous Two-Parameter Abstract Cauchy Problem

inhomogeneous two-parameter abstract cauchy problem

Factoring Weakly Compact Operators and the Inhomogeneous Cauchy Problem

By using the technique of factoring weakly compact operators through reflexive Banach spaces we prove that a class of ordinary differential equations with Lipschitz continuous perturbations has a strong solution when the problem is governed by a closed linear operator generating a strongly continuous semigroup of compact operators.

Banach space valued ultradistributions and applications to abstract Cauchy problems

We define the convolution of Banach space valued ultradistributions in the sense of Braun, Meise, and Taylor. We then treat abstract Cauchy problems in Banach spaces as convolution equations and give a characterization of those problems that have ultradistributional fundamental solutions. Our characterization extends in the Beurling case a result due to H.A. Emamirad. We apply our result to dif...