Browsing by Author "Klun, Giuliano"

Now showing 1 - 8 of 8
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    Non-well-ordered lower and upper solutions for semilinear systems of PDEs
    (SISSA, 2020-05) Fonda, Alessandro; Klun, Giuliano; Sfecci, Andrea
    We prove existence results for systems of boundary value problems involving elliptic second order differential operators. The as-sumptions involve lower and upper solutions, which may be either well-ordered, or not at all. The results are stated in an abstract framework, and can be translated also for systems of parabolic type.
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    On Dini derivatives of real functions
    (2021) Fonda, Alessandro; Klun, Giuliano; Sfecci, Andrea; mathematics
    For a continuous function f, the set Vf made of those points where the lower left derivative is strictly less than the upper right derivative is totally disconnected. Besides continuity, alternative assumptions are proposed so to preserve this property. On the other hand, we construct a function f whose set Vf coincides with the entire domain, and nevertheless f is continuous on an infinite set, possibly having infinitely many cluster points. Some open problems are proposed.
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    On functions having coincident ρ-norms
    (SISSA, 2019-03-25) Klun, Giuliano
    In a measure space (X;A; μ) we consider two measurable functions ƒ; g : E → R for some E ∈ A. We characterize the property of having equal p-norms when ρ varies in an infinite set P in [1;+∞). In a first theorem we consider the case of bounded functions when P is unbounded with ∑p∈P(1/p) = +∞ . The second theorem deals with the possibility of unbounded functions, when P has a finite accumulation point in [1, + ∞ ).
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    On the Dirichlet problem associated to bounded perturbations of positively-(p, q)-homogeneous Hamiltonian systems
    (2022-02-21) Fonda, Alessandro; Klun, Giuliano; Obersnel, Franco; Sfecci, Andrea; mathematics
    The existence of solutions for the Dirichlet problem associated to bounded perturbations of positively-(p, q)-homogeneous Hamiltonian sys tems is considered both in nonresonant and resonant situations. In order to deal with the resonant case, the existence of a couple of lower and up per solutions is assumed. Both the well-ordered and the non-well-ordered cases are analysed. The proof is based on phase-plane analysis and topo logical degree theory
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    On the topological degree of planar maps avoiding normal cones
    (SISSA, 2019-03-07) Fonda, Alessandro; Klun, Giuliano; Mathematics
    The classical Poincaré–Bohl theorem provides the exis-tence of a zero for a function avoiding external rays. When the do-main is convex, the same holds true when avoiding normal cones. We consider here the possibility of dealing with nonconvex sets having in-ward corners or cusps, in which cases the normal cone vanishes. This allows us to deal with situations where the topological degree may be di˙erent from ±1.
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    Periodic solutions of nearly integrable Hamiltonian systems bifurcating from infinite-dimensional tori
    (2019-09-12) Fonda, Alessandro; Klun, Giuliano; Sfecci, Andrea
    We prove the existence of periodic solutions of some infinite-dimensional nearly integrable Hamiltonian systems, bifurcating from infinite-dimensional tori, by the use of a generalization of the Poincaré–Birkhoff Theorem.
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    Periodic solutions of second order differential equations in Hilbert spaces
    (SISSA, 2020-05) Fonda, Alessandro; Klun, Giuliano; Sfecci, Andrea
    We prove the existence of periodic solutions of some infinite-dimensional systems by the use of the lower/upper solutions method. Both the well-ordered and non-well-ordered cases are treated, thus generalizing to systems some well established results for scalar equations.
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    Well-ordered and non-well-ordered lower and upper solutions for periodic planar systems
    (2021-01-08) Fonda, Alessandro; Klun, Giuliano; Sfecci, Andrea; mathematics
    The aim of this paper is to extend the theory of lower and upper solutions to the periodic problem associated with planar systems of differential equations. We generalize previously given definitions and we are able to treat both the well-ordered case and the non-well-ordered case. The proofs involve topological degree arguments, together with a detailed analysis of the solutions in the phase plane.