7 papers
Solvability of abstract semilinear equations by a global diffeomorphism theorem
Michal Beldzinski, Marek Galewski, Robert Steglinski
In this work we proivied a new simpler proof of the global diffeomorphism theorem from [9] which we further apply to consider unique solvability of some abstract semilinear equatio…
Parametric critical point theorems and their applications to boundary value problems on the Sierpiński Gasket
Marek Galewski, Mateusz Krukowski
In this note we consider the classical variational tools like: Ekelenad's Variational Principle, Mountain Pass Lemma and some of their corollaries subject to a parameter. Next, we…
Global diffeomorphism theorem applied to the solvability of discrete and continuous boundary value problems
Michał Bełdziński, Marek Galewski
We investigate solvability of a continuous Dirichlet boundary value problem together with its classical discretization using a gobal diffeomorphism theorem.
Existence and multiplicity results for boundary value problems connected with the discrete p(.)-Laplacian on weighted finite graphs
Marek Galewski, Renata Wieteska
We use the direct variational method, the Ekeland variational principle, the mountain pass geometry and Karush-Kuhn-Tucker theorem in order to investigate existence and multiplicit…
A critical point theorem on a closed ball and some applications to boundary value problems
Marek Galewski
We consider a functional being a difference of two differentiable convex functionals on a closed ball. Existence and multiplicity of critical points is investigated. Some applicati…
A note on a global invertibility of mappings on
Marek Galewski
We provide sufficient conditions for a mapping to be a global diffeomorphism in case it is strictly (Hadamard) differentiable. We use classical local inv…