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Browsing by Subject "fixed point index"

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    Item type:Article, Access status: Open Access ,
    A study of chaos for processes under small perturbations II - rigorous proof of chaos
    (2010) Oprocha, Piotr; Wilczyński, Paweł
    In the present paper we prove distributional chaos for the Poincaré map in the perturbed equation $\dot{z}=\left(1 + e^{i\kappa t} |z|^2\right)\bar{z}^2 - N e^{-i\frac{\pi}{3}}.$ Heteroclinic and homoclinic connections between two periodic solutions bifurcating from the stationary solution $0$ present in the system when $N = 0$ are also discussed.
  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    On a fixed point theorem for operator systems and eigenvalue criteria for existence of positive solutions
    (Wydawnictwa AGH, 2026) Fernández-Pardo, Laura M.; Rodríguez-López, Jorge
    We provide an alternative approach, based on the Leray-Schauder fixed point index in cones, to a fixed point theorem for operator systems due to Precup. Our focus is on the case of operators whose components are entirely of compressive type. The abstract technique is applied to a system of second-order differential equations providing a coexistence positive solution by means of an eigenvalue type criterion.