Perturbations associated with hypergeometric cauchy problems

Abstract

Two types of perturbation theorems are proved for Cauchy problem thta involve abstract generalized hypergeometric equations of the form

in some Banach Space X. One of these involves a perturbation on a β type factor while the other trats an α type Factor. Under appropriate boundeness and continuity assumptions, the pertubed solutions are shown to degenerate regularly in norm to the solution of the unperturbed problems.

Keywords:

• Pertubation
• Banach space
• Related differential equations
• Degenerates regularly
• Post-Widder formula

AMS(MOS)Subject Classification:

• Primary 34E10
• Secondary 34G05