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Conditions for having a diffeomorphism between two Banach spaces
(Department of Mathematics - Texas State University, 2014)
We provide sufficient conditions for a mapping acting between two Banach spaces to be a diffeomorphism. Standart arguments allow us to obtain a local diffeomorphism. It is proved to be global using mountain pass geometry.
On a new critical point theorem and some applications to discrete equations
(AGH University of Science and Technology Press, 2014)
Using the Fenchel-Young duality we derive a new critical point theorem. We illustrate our results with solvability for certain discrete BVP. Multiple solutions are also considered.