×

A note on singular and degenerate abstract equations. (English) Zbl 0533.47015

The author investigates the equation \((BA_ 1+A_ 0)u=h\) where h is given in the complex Banach space \(E\), \(u\) is the solution to be found in the complex Banach space \(F\), and \(B\), \(A_ i(i=0,1)\) are suitable closed linear operators from E into itself, and from \(F\) into \(E\), respectively. Conditions are obtained for the existence and uniqueness of a solution to the above equation. No proofs are given. Two applications to degenerate differential problems in a Banach space setting are included; for related problems the reader is referred to R. W. Carroll and R. E. Showalter, Singular and degenerate Cauchy problems (1976).
Reviewer: R.W.Cross

MSC:

47A50 Equations and inequalities involving linear operators, with vector unknowns
47E05 General theory of ordinary differential operators
47F05 General theory of partial differential operators
PDFBibTeX XMLCite