7 papers
A Frobenius Theorem on Fréchet Manifolds
Kaveh Eftekharinasab
We investigate the integrability of Fréchet tangent distributions on Fréchet manifolds. We introduce the local well-posedness Condition W for split tangent subbundles, which redu…
A Class of Functionals on the Sequence Space Satisfying the Palais-Smale Condition
Kaveh Eftekharinasab
We introduce a class of functionals on the space of rapidly decreasing sequences , called -functionals, defined as decomposable sums of quadratic and convex terms…
Spray-Invariant Sets in Infinite-Dimensional Manifolds
Kaveh Eftekharinasab
We introduce the concept of spray-invariant sets on infinite-dimensional manifolds, where any geodesic of a spray starting in the set stays within it for its entire domain. These s…
On the existence of a global diffeomorphism between Fréchet spaces
Kaveh Eftekharinasab
We provide sufficient conditions for the existence of a global diffeomorphism between tame Fréchet spaces. We prove a version of the Mountain Pass Theorem which is a key ingredien…
A Generalized Palais-Smale Condition in the Fréchet space setting
Kaveh Eftekharinasab
We extend the Palais-Smale condition to Keller's -functionals on Fréchet spaces. Using this condition together with Ekeland's variational principle, we obtain some results…
Global Implicit Function Theorems and Critical Point Theory in Fréchet Spaces
Kaveh Eftekharinasab
We prove two versions of a global implicit function theorem, which involve no loss of derivative, for Keller's -mappings between arbitrary Fréchet spaces. Subsequently, w…