Existence and quasilinearization in Hilbert spaces revisited

Abstract

In this article we adjust and correct some proofs that appeared in the article (El-Gebeily, M. and O'Regan, D., 2006, Existence and quasilinearization methods in Hilbert spaces, Journal of Mathematical Analysis and Applications, 324, 344–357) in connection with the abstract operator problem in a Hilbert space . Both existence results and abstract quasilinearization are adjusted and better streamlined.

Keywords:

• Self adjoint operators
• Nonlinear operators
• Existence
• Quasilinearization methods

Keywords:

• 2000 Mathematics Subject Classifications: 41A65
• 47J05
• 47J25

Acknowledgment

Research for the first author has been funded by King Fahd University of Petroleum and Minerals under Project number MS/Singular ODE/274.