Ekeland's inverse function theorem in graded Fréchet spaces revisited for multifunctions
Copyright policy )Ekeland's inverse function theorem in graded Fréchet spaces revisited for multifunctions
In this paper, we present some implicit function theorems for set-valued mappings between Fréchet 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 Fréchet spaces with non-smooth data is given.
Revised version
- Pedagogical University Mozambique
- University of Limoges France
- Q University Kazakhstan
- Department of Mathematics
- Federation University Australia
Applications of operator theory to differential and integral equations, Abstract inverse mapping and implicit function theorems involving nonlinear operators, Ekeland's variational principle, Linear differential equations in abstract spaces, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Fréchet space, Variational and other types of inclusions, contingent derivative, implicit multifunction theorem, inverse function theorem, Nash-Moser theorem, Graded Fréchet spaces and tame operators, Set-valued operators
Applications of operator theory to differential and integral equations, Abstract inverse mapping and implicit function theorems involving nonlinear operators, Ekeland's variational principle, Linear differential equations in abstract spaces, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Fréchet space, Variational and other types of inclusions, contingent derivative, implicit multifunction theorem, inverse function theorem, Nash-Moser theorem, Graded Fréchet spaces and tame operators, Set-valued operators
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