5 papers
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…
Weighted spaces on nilpotent, locally compact groups
Mateusz Krukowski
Our paper begins with a revision of spectral theory for commutative Banach algebras, which enables us to prove the conjecture for locally compact abelian groups. We follow…
Darbo-type theorem for quasimeasure of noncompactness
Mateusz Krukowski
The paper introduces the concept of quasimeasure of noncompactness. Motivated by the Arzelà-Ascoli theorem for , where is an Euclidean space and an arbitrary Bana…
Arzelà-Ascoli theorem in uniform spaces
Mateusz Krukowski
In the paper, we generalize the Arzelà-Ascoli theorem in the setting of uniform spaces. At first, we recall well-known facts and theorems coming from monographs of Kelley and Willa…
Compactness result and its applications in integral equations
Mateusz Krukowski, Bogdan Przeradzki
A version of Arzelà-Ascoli theorem for being -locally compact Hausdorff space is proved. The result is used in proving compactness of Fredholm, Hammerstein and Urysohn opera…