Ekeland's inverse function theorem in graded Frechet spaces revisited for multifunctions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:457

Article

Van Ngai, Huynh¹  Thera, Michel^2,3 

[1] Univ Quynhon, Dept Math, Quynhon, Vietnam

[2] Univ Limoges, Lab XLIM, UMR CNRS 6172, Limoges, France

[3] Federat Univ Australia, Ctr Informat & Appl Optimizat, Ballarat, Vic, Australia

关键词: Inverse function theorem;    Frechet space;    Nash-Moser theorem;    Contingent derivative;    Ekeland's variational principle;    Implicit multifunction theorem;   

DOI  :  10.1016/j.jmaa.2017.07.040

来源: Elsevier

【 摘 要 】

In this paper, we present some inverse function theorems and implicit function theorems for set-valued mappings between Frechet spaces. The proof relies on Lebesgue's Dominated Convergence Theorem and on Ekeland's variational principle. An application to the existence of solutions of differential equations in Frechet spaces with non-smooth data is given. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free