General solvability theorems

Mieczyslaw Altman

Vol. 75 (1978), No. 1, 1–14

DOI: 10.2140/pjm.1978.75.1

Abstract

A further development of the method of contractor directions is presented. In order to make the method applicable to applied problems, certain conditions are imposed on the sets of contractor directions. This in turn requires a more sophisticated transfinite induction argument. In terms of contractor directions, sufficient conditions are given for existence of solutions of nonlinear operator equations in Banach spaces.

Mathematical Subject Classification

Primary: 47H15

Milestones

Received: 1 April 1976

Revised: 22 June 1977

Published: 1 March 1978