Maciej Starostka - Publikacje - MOST Wiedzy

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Zdjęcie profilowe: dr inż. Maciej Starostka

dr inż. Maciej Starostka

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wszystkich: 11

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Katalog Publikacji

Rok 2023
Rok 2022
  • On a comparison principle and the uniqueness of spectral flow
    Publikacja

    - MATHEMATISCHE NACHRICHTEN - Rok 2022

    The spectral flow is a well-known quantity in spectral theory that measures the variation of spectra about 0 along paths of selfadjoint Fredholm operators. The aim of this work is twofold. Firstly, we consider homotopy invariance properties of the spectral flow and establish a simple formula which comprises its classical homotopy invariance and yields a comparison theorem for the spectral flow under compact perturbations. We apply...

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Rok 2021
Rok 2020
Rok 2019
  • Bernstein-type theorem for ϕ-Laplacian

    In this paper we obtain a solution to the second-order boundary value problem of the form \frac{d}{dt}\varPhi'(\dot{u})=f(t,u,\dot{u}), t\in [0,1], u\colon \mathbb {R}\to \mathbb {R} with Sturm–Liouville boundary conditions, where \varPhi\colon \mathbb {R}\to \mathbb {R} is a strictly convex, differentiable function and f\colon[0,1]\times \mathbb {R}\times \mathbb {R}\to \mathbb {R} is continuous and satisfies a suitable growth...

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  • The E-Cohomological Conley Index, Cup-Lengths and the Arnold Conjecture on T 2n
    Publikacja

    - ADVANCED NONLINEAR STUDIES - Rok 2019

    We show that the E-cohomological Conley index, that was introduced by the first author recently, has a natural module structure. This yields a new cup-length and a lower bound for the number of critical points of functionals on Hilbert spaces. When applied to the setting of the Arnold conjecture, this paves the way to a short proof on tori, where it was first shown by C. Conley and E. Zehnder in 1983.

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Rok 2017
  • E-cohomological Conley index
    Publikacja

    - Rok 2017

    In this thesis we continue with developing the E-cohomological Conley index which was introduced by A.Abbondandolo. In particular, we generalize the index to non-gradient flows, we show that it an possesses additional multiplicative structure and we prove the continuation principle. Then, using continuation principle, we show how the computation of the E-cohomological Conley index can be reduced to the computation of the classical...

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  • Homotopy invariance of the Conley index and local Morse homology in Hilbert spaces
    Publikacja

    - JOURNAL OF DIFFERENTIAL EQUATIONS - Rok 2017

    In this paper we introduce a new compactness condition — Property-(C) — for flows in (not necessary locally compact) metric spaces. For such flows a Conley type theory can be developed. For example (regular) index pairs always exist for Property-(C) flows and a Conley index can be defined. An important class of flows satisfying the this compactness condition are LS-flows. We apply E-cohomology to index pairs of LS-flows and obtain...

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Rok 2015
Rok 2012

wyświetlono 1917 razy