@article {2021, title = {On Dini derivatives of real functions}, year = {2021}, author = {Giuliano Klun and Alessandro Fonda and Andrea Sfecci} } @article {2021, title = {Non-well-ordered lower and upper solutions for semilinear systems of PDEs}, journal = {Communications in Contemporary MathematicsCommunications in Contemporary Mathematics}, year = {2021}, month = {2021/08/27}, pages = {2150080}, abstract = {

We prove existence results for systems of boundary value problems involving elliptic second-order differential operators. The assumptions 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.We prove existence results for systems of boundary value problems involving elliptic second-order differential operators. The assumptions 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.

}, isbn = {0219-1997}, url = {https://doi.org/10.1142/S0219199721500802}, author = {Alessandro Fonda and Giuliano Klun and Andrea Sfecci} } @article {2021, title = {Periodic Solutions of Second-Order Differential Equations in Hilbert Spaces}, volume = {18}, year = {2021}, month = {2021/09/07}, pages = {223}, abstract = {

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.

}, isbn = {1660-5454}, url = {https://doi.org/10.1007/s00009-021-01857-8}, author = {Alessandro Fonda and Giuliano Klun and Andrea Sfecci} } @article {2021, title = {Well-Ordered and Non-Well-Ordered Lower and Upper Solutions for Periodic Planar Systems}, journal = {Advanced Nonlinear Studies}, volume = {21}, year = {2021}, month = {2021}, pages = {397 - 419}, url = {https://doi.org/10.1515/ans-2021-2117}, author = {Alessandro Fonda and Giuliano Klun and Andrea Sfecci} } @article {2020, title = {Periodic solutions of nearly integrable Hamiltonian systems bifurcating from infinite-dimensional tori}, journal = {NONLINEAR ANALYSIS}, year = {2020}, abstract = {

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 Poincar{\'e}{\textendash}Birkhoff Theorem.

}, issn = {0362-546X}, doi = {10.1016/j.na.2019.111720}, url = {https://doi.org/10.1016/j.na.2019.111720}, author = {Alessandro Fonda and Giuliano Klun and Andrea Sfecci} } @article {2019, title = {On the topological degree of planar maps avoiding normal cones}, journal = {TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS}, volume = {53}, number = {SISSA;04/2019/MATE}, year = {2019}, pages = {825-845}, publisher = {SISSA}, abstract = {

The classical Poincar{\'e}-Bohl theorem provides the existence of a zero for a function avoiding external rays. When the domain is convex, the same holds true when avoiding normal cones.
We consider here the possibility of dealing with nonconvex sets having inward corners or cusps, in which cases the normal cone vanishes. This allows us to deal with situations where the topological degree may be strictly greater than $1$.

}, issn = {1230-3429}, doi = {10.12775/TMNA.2019.034}, url = {http://dx.doi.org/10.12775/TMNA.2019.034}, author = {Alessandro Fonda and Giuliano Klun} } @article {FONDA20171064, title = {An avoiding cones condition for the Poincar{\'e}{\textendash}Birkhoff Theorem}, journal = {Journal of Differential Equations}, volume = {262}, number = {2}, year = {2017}, pages = {1064 - 1084}, abstract = {

We provide a geometric assumption which unifies and generalizes the conditions proposed in [11], [12], so to obtain a higher dimensional version of the Poincar{\'e}{\textendash}Birkhoff fixed point Theorem for Poincar{\'e} maps of Hamiltonian systems.

}, keywords = {Avoiding cones condition, Hamiltonian systems, Periodic solutions, Poincar{\'e}{\textendash}Birkhoff theorem}, issn = {0022-0396}, doi = {https://doi.org/10.1016/j.jde.2016.10.002}, url = {http://www.sciencedirect.com/science/article/pii/S0022039616303278}, author = {Alessandro Fonda and Paolo Gidoni} } @article {Fonda2016, title = {Generalizing the Poincar{\'e}{\textendash}Miranda theorem: the avoiding cones condition}, journal = {Annali di Matematica Pura ed Applicata (1923 -)}, volume = {195}, number = {4}, year = {2016}, month = {Aug}, pages = {1347{\textendash}1371}, abstract = {

After proposing a variant of the Poincar{\'e}{\textendash}Bohl theorem, we extend the Poincar{\'e}{\textendash}Miranda theorem in several directions, by introducing an avoiding cones condition. We are thus able to deal with functions defined on various types of convex domains, and situations where the topological degree may be different from \$\$\backslashpm \$\${\textpm}1. An illustrative application is provided for the study of functionals having degenerate multi-saddle points.

}, issn = {1618-1891}, doi = {10.1007/s10231-015-0519-6}, url = {https://doi.org/10.1007/s10231-015-0519-6}, author = {Alessandro Fonda and Paolo Gidoni} } @article {fonda2016periodic, title = {Periodic perturbations of Hamiltonian systems}, journal = {Advances in Nonlinear Analysis}, volume = {5}, number = {4}, year = {2016}, pages = {367{\textendash}382}, publisher = {De Gruyter}, abstract = {

We prove existence and multiplicity results for periodic solutions of Hamiltonian systems, by the use of a higher dimensional version of the Poincar{\'e}{\textendash}Birkhoff fixed point theorem. The first part of the paper deals with periodic perturbations of a completely integrable system, while in the second part we focus on some suitable global conditions, so to deal with weakly coupled systems.

}, doi = {10.1515/anona-2015-0122}, author = {Alessandro Fonda and Maurizio Garrione and Paolo Gidoni} } @article {FONDA201573, title = {A permanence theorem for local dynamical systems}, journal = {Nonlinear Analysis: Theory, Methods \& Applications}, volume = {121}, year = {2015}, note = {Nonlinear Partial Differential Equations, in honor of Enzo Mitidieri for his 60th birthday}, pages = {73 - 81}, abstract = {

We provide a necessary and sufficient condition for permanence related to a local dynamical system on a suitable topological space. We then present an illustrative application to a Lotka{\textendash}Volterra predator{\textendash}prey model with intraspecific competition.

}, keywords = {Lotka{\textendash}Volterra, permanence, Predator{\textendash}prey, Uniform persistence}, issn = {0362-546X}, doi = {https://doi.org/10.1016/j.na.2014.10.011}, url = {http://www.sciencedirect.com/science/article/pii/S0362546X14003332}, author = {Alessandro Fonda and Paolo Gidoni} } @article {fonda2013, title = {Generalized Sturm-Liouville boundary conditions for first order differential systems in the plane}, journal = {Topol. Methods Nonlinear Anal.}, volume = {42}, number = {2}, year = {2013}, pages = {293{\textendash}325}, publisher = {Nicolaus Copernicus University, Juliusz P. Schauder Centre for Nonlinear Studies}, abstract = {

We study asymptotically positively homogeneous first order systems in the plane, with boundary conditions which are positively homogeneous, as well. Defining a generalized concept of Fu{\v c}{\'\i}k spectrum which extends the usual one for the scalar second order equation, we prove existence and multiplicity of solutions. In this way, on one hand we extend to the plane some known results for scalar second order equations (with Dirichlet, Neumann or Sturm-Liouville boundary conditions), while, on the other hand, we investigate some other kinds of boundary value problems, where the boundary points are chosen on a polygonal line, or in a cone. Our proofs rely on the shooting method.

}, url = {https://projecteuclid.org:443/euclid.tmna/1461248981}, author = {Alessandro Fonda and Maurizio Garrione} } @article {fonda2013periodic, title = {Periodic bouncing solutions for nonlinear impact oscillators}, journal = {Advanced Nonlinear Studies}, volume = {13}, number = {1}, year = {2013}, pages = {179{\textendash}189}, publisher = {Advanced Nonlinear Studies, Inc.}, doi = {10.1515/ans-2013-0110}, author = {Alessandro Fonda and Andrea Sfecci} } @article {FONDA20121369, title = {A general method for the existence of periodic solutions of differential systems in the plane}, journal = {Journal of Differential Equations}, volume = {252}, number = {2}, year = {2012}, pages = {1369 - 1391}, abstract = {

We propose a general method to prove the existence of periodic solutions for planar systems of ordinary differential equations, which can be used in many different circumstances. Applications are given to some nonresonant cases, even for systems with superlinear growth in some direction, or with a singularity. Systems {\textquotedblleft}at resonance{\textquotedblright} are also considered, provided a Landesman{\textendash}Lazer type of condition is assumed.

}, keywords = {Nonlinear dynamics, Periodic solutions}, issn = {0022-0396}, doi = {https://doi.org/10.1016/j.jde.2011.08.005}, url = {http://www.sciencedirect.com/science/article/pii/S0022039611003196}, author = {Alessandro Fonda and Andrea Sfecci} } @article {fonda2012, title = {Periodic solutions of a system of coupled oscillators with one-sided superlinear retraction forces}, journal = {Differential Integral Equations}, volume = {25}, number = {11/12}, year = {2012}, month = {11}, pages = {993{\textendash}1010}, publisher = {Khayyam Publishing, Inc.}, url = {https://projecteuclid.org:443/euclid.die/1356012248}, author = {Alessandro Fonda and Andrea Sfecci} } @article {FONDA20111052, title = {Double resonance with Landesman{\textendash}Lazer conditions for planar systems of ordinary differential equations}, journal = {Journal of Differential Equations}, volume = {250}, number = {2}, year = {2011}, pages = {1052 - 1082}, abstract = {

We prove the existence of periodic solutions for first order planar systems at resonance. The nonlinearity is indeed allowed to interact with two positively homogeneous Hamiltonians, both at resonance, and some kind of Landesman{\textendash}Lazer conditions are assumed at both sides. We are thus able to obtain, as particular cases, the existence results proposed in the pioneering papers by Lazer and Leach (1969) [27], and by Frederickson and Lazer (1969) [18]. Our theorem also applies in the case of asymptotically piecewise linear systems, and in particular generalizes Fabry{\textquoteright}s results in Fabry (1995) [10], for scalar equations with double resonance with respect to the Dancer{\textendash}Fu{\v c}ik spectrum.

}, keywords = {Double resonance, Landesman{\textendash}Lazer conditions, Nonlinear planar systems}, issn = {0022-0396}, doi = {https://doi.org/10.1016/j.jde.2010.08.006}, url = {http://www.sciencedirect.com/science/article/pii/S0022039610002901}, author = {Alessandro Fonda and Maurizio Garrione} } @article {fonda2011nonlinear, title = {Nonlinear resonance: a comparison between Landesman-Lazer and Ahmad-Lazer-Paul conditions}, journal = {Advanced Nonlinear Studies}, volume = {11}, number = {2}, year = {2011}, pages = {391{\textendash}404}, publisher = {Advanced Nonlinear Studies, Inc.}, abstract = {

We show that the Ahmad-Lazer-Paul condition for resonant problems is more general than the Landesman-Lazer one, discussing some relations with other existence conditions, as well. As a consequence, such a relation holds, for example, when considering resonant boundary value problems associated with linear elliptic operators, the p-Laplacian and, in the scalar case, with an asymmetric oscillator.

}, doi = {10.1515/ans-2011-0209}, author = {Alessandro Fonda and Maurizio Garrione} }