Alessandro Fonda's publications
1. A.
Cellina, G. Colombo and A. Fonda,
Approximate selections and fixed points for upper semicontinuous maps
with decomposable values,
Proceedings of the American Mathematical Society 98 (1986), 663-666.
2. A.
Fonda,
Guiding functions and periodic solutions to functional differential
equations,
Proceedings of the American Mathematical Society 99 (1987), 79-85.
3. A.
Fonda and F. Zanolin,
Periodic solutions of second order differential equations of Liénard
type with jumping nonlinearities,
Commentationes Mathematicae Universitatis Carolinae 28 (1987), 33-41.
4. A.
Cellina, G. Colombo and A. Fonda,
A
continuous version of Liapunov's convexity theorem,
Annales de l'Institut H. Poincaré, Analyse non lineaire 5 (1988), 23-36.
5. A.
Fonda,
Uniformly persistent semidynamical systems,
Proceedings of the American Mathematical Society 104 (1988), 111-116.
6. G.
Colombo, A. Fonda and A. Ornelas,
Lower
semicontinuous perturbations of maximal monotone differential
inclusions,
Israel Journal of Mathematics 61 (1988), 211-218.
7. A.
Fonda,
Variational problems at resonance without monotonicity,
Bulletin de l'Académie Royale Scientifique de Belgique LXXIV (1988),
54-63.
8. A.
Fonda and D. Lupo,
Periodic solutions of second order ordinary differential equations,
Bollettino dell'Unione Matematica Italiana (7) 3-A (1989), 291-299.
9. A.
Fonda and P. Habets,
Periodic solutions of asymptotically positively homogeneous differential
equations,
Journal of Differential Equations 81 (1989), 68-97.
10. A.
Fonda and J. Mawhin,
Quadratic forms, weighted eigenfunctions and boundary value problems for
non-linear second order ordinary differential equations,
Proceedings of the Royal Society of Edinburgh 112A (1989), 145-153.
11. A.
Fonda and M. Willem,
Subharmonic oscillations of forced pendulum-type equations,
Journal of Differential Equations 81 (1989), 215-220.
12. A.
Fonda and J. P. Gossez,
Semicoercive variational problems at resonance: an abstract approach,
Differential and Integral Equations 3 (1990), 695-708 (contact
me for more information).
13. C.
Fabry and A. Fonda,
Periodic solutions of nonlinear differential equations with double
resonance,
Annali di Matematica Pura e Applicata (IV) 157 (1990), 99-116.
14. A.
Fonda, J. P. Gossez and F. Zanolin,
On a
nonresonance condition for a semilinear elliptic problem,
Differential and Integral Equations 4 (1991), 945-951 (contact
me for more information).
15. A.
Fonda and A. C. Lazer,
Subharmonic solutions of conservative systems with nonconvex potentials,
Proceedings of the American Mathematical Society 115 (1992), 183-190.
16. A.
Fonda and F. Zanolin,
On the use of time-maps for
the solvability of nonlinear boundary value problems,
Archive der Mathematik 59 (1992), 245-259.
17. A.
Fonda and J. Mawhin,
Critical point theory and
multiple periodic solutions of conservative systems with periodic
nonlinearity,
in:
"The Problem of Plateau: a Tribute to J. Douglas and T. Rado",
T. M.
Rassias ed., World Scientific, London, 1992, pp. 111-128.
Also published as:
Multiple periodic solutions of conservative systems with periodic
nonlinearity,
in:
Differential equations and applications, Vol. I, II (Columbus, OH, 1988),
298-304, Ohio Univ. Press, Athens, OH, 1989.
18. C.
Fabry and A. Fonda,
Nonlinear equations at resonance and generalized eigenvalue problems,
Nonlinear Analysis, Theory, Methods and Applications 18 (1992), 427-444.
19. A.
Fonda and J. Mawhin,
Iterative and variational methods for the solvability of some semilinear
equations in Hilbert spaces,
Journal of Differential Equations 98 (1992), 355-375.
20. A.
Fonda and J. Mawhin,
An
iterative method for the solvability of semilinear equations in Hilbert
spaces and applications,
in:
"Partial Differential Equations and Other Topics",
J.
Wiener and J. K. Hale eds., Longman, London, 1992, pp. 126-132.
21. A.
Fonda, M. Ramos and M. Willem,
Subharmonic solutions for second order differential equations,
Topological Methods in Nonlinear Analysis 1 (1993), 49-66.
22. A.
Fonda,
On
the existence of periodic solutions for scalar second order differential
equations when only the
asymptotic behaviour of the potential is known,
Proceedings of the American Mathematical Society 119 (1993), 439-445.
23. C.
Fabry, A. Fonda and F. Munjamarere,
Semilinear equations at resonance with non-symmetric linear part,
Journal of Mathematical Analysis and Applications 180 (1993), 189-206.
24. A.
Fonda, R. Manasevich and F. Zanolin,
Subharmonic solutions for some second order differential equations with
singularities,
SIAM
Journal of Mathematical Analysis 24 (1993), 1294-1311.
25. A.
Fonda,
Periodic solutions of scalar second order differential equations with a
singularity,
Memoire de la Classe de Sciences de l'Académie Royale Scientifique de
Belgique, tome IV, 1993.
26. A.
Fonda and M. Ramos,
Large-amplitude subharmonic oscillations for scalar second order
differential equations with asymmetric nonlinearities,
Journal of Differential Equations 109 (1994), 354-372.
27. A.
Fonda, Z. Schneider and F. Zanolin,
Periodic oscillations for a nonlinear suspension bridge model,
Journal of Computational and Applied Mathematics 52 (1994), 113-140.
28. A.
Fonda,
Periodic solutions for a conservative system of differential equations
with a singularity of repulsive type,
Nonlinear Analysis, Theory, Methods and Applications 24 (1995), 667-676.
29. A.
Fonda and F. Zanolin,
Periodic oscillations of forced pendulums with a very small length,
Proceedings of the Royal Society of Edinburgh 127A (1997), 67-76.
30. P.
Buttazzoni and A. Fonda,
Periodic perturbations of scalar second order differential equations,
Discrete and Continuous Dynamical Systems 3 (1997), 451-455.
31. A.
Fonda and F. Zanolin,
Bounded solutions of nonlinear second order ordinary differential
equations,
Discrete and Continuous Dynamical Systems 4 (1998), 91-98.
32. C.
Fabry and A. Fonda,
Nonlinear resonance in asymmetric oscillators,
Journal of Differential Equations 147 (1998), 58-78.
33. A.
Fonda and R. Ortega,
Positively homogeneous equations in the plane,
Discrete and Continuous Dynamical Systems 6 (2000), 475-482.
34. C.
Fabry and A. Fonda,
Bifurcations from infinity in asymmetric nonlinear oscillators,
NoDEA
- Nonlinear Differential Equations and Applications 7 (2000), 23-42.
35. A.
Fonda and P. Torres,
Multiple solutions of
positively homogeneous equations,
Nonlinear
Analysis,
Theory, Methods and Applications 49 (2002), 1137-1147.
36. A.
Fonda,
Positively homogeneous
hamiltonian systems in the plane,
Journal of Differential
Equations 200 (2004), 162-184.
37. C.
Fabry and A. Fonda,
Periodic solutions of
perturbed isochronous hamiltonian systems at resonance,
Journal of Differential
Equations 214 (2005), 299-325.
38. C.
Fabry and A. Fonda,
Unbounded motions of perturbed
isochronous hamiltonian systems at resonance,
Advanced Nonlinear Studies 5
(2005), 351-373.
39. A.
Fonda,
Topological degree and
generalized asymmetric oscillators,
Topological Methods in
Nonlinear Analysis 28 (2006), 171-188.
40. A.
Fonda and J. Mawhin,
Planar
differential systems at resonance,
Advances
in Differential Equations 11 (2006), 1111-1133 (contact
me for more information).
41. A.
Fonda and R. Toader,
Periodic
orbits of radially symmetric Keplerian-like systems: a topological
degree approach,
Journal of
Differential Equations 244 (2008), 3235-3264.
42. A.
Fonda and R. Toader,
Nonlinear
perturbations of some non-invertible differential operators,
Differential
and Integral Equations 22 (2009), 949-978 (contact
me for more information).
43. A.
Fonda and L. Ghirardelli,
Multiple periodic
solutions of scalar second order differential equations,
Nonlinear Analysis, Theory,
Methods and Applications 72 (2010), 4005-4015.
44. A.
Fonda and L. Ghirardelli,
Multiple periodic
solutions of Hamiltonian systems in the plane,
Topological Methods in
Nonlinear Analysis 36 (2010), 27-38.
45. A.
Fonda and A. Ureña,
Periodic,
subharmonic, and quasi-periodic oscillations under the action of a
central force,
Discrete and Continuous
Dynamical Systems 29 (2011), 169-192.
46. A.
Fonda and M. Garrione,
Double resonance with
Landesman-Lazer conditions for planar systems of ordinary differential
equations,
Journal of Differential
Equations 250 (2011), 1052-1082.
47. A.
Fonda and R. Toader,
Radially symmetric systems with
a singularity and asymptotically linear growth,
Nonlinear Analysis, Theory,
Methods and Applications 74 (2011), 2485-2496.
48. A.
Fonda and M. Garrione,
Nonlinear resonance:
a comparison between Landesman-Lazer and Ahmad-Lazer-Paul conditions,
Advanced Nonlinear Studies 11
(2011), 391-404.
49. A.
Fonda and R. Toader,
Lower and upper
solutions to semilinear boundary value problems: an abstract approach,
Topological Methods in
Nonlinear Analysis 38 (2011), 59-94.
50. A.
Fonda and R. Toader,
Periodic orbits of
radially symmetric systems with a singularity: the repulsive case,
Advanced Nonlinear Studies 11
(2011), 853-874.
51. A.
Fonda and A. Sfecci,
A general method for the
existence of periodic solutions of differential equations in the plane,
Journal of Differential
Equations 252 (2012), 1369-1391.
52. A.
Fonda and R. Toader,
Periodic solutions of
radially symmetric perturbations of Newtonian systems,
Proceedings of the American
Mathematical Society 140 (2012), 1331-1341.
53. A.
Fonda, R. Toader and F. Zanolin,
Periodic solutions of singular
radially symmetric systems with superlinear growth,
Annali di Matematica Pura ed
Applicata 191 (2012), 181-204.
54. A.
Fonda and R. Toader,
Periodic solutions of
pendulum-like Hamiltonian systems in the plane,
Advanced Nonlinear Studies 12 (2012),
395-408.
55. A.
Boscaggin, A. Fonda and M. Garrione,
A multiplicity result for
periodic solutions of second order differential equations with a
singularity,
Nonlinear Analysis, Theory,
Methods and Applications 75 (2012), 4457-4470.
56. A.
Fonda, R. Toader and P. J. Torres,
Periodic motions in a
gravitational central field with a rotating external force,
Celestial Mechanics and
Dynamical Astronomy 113 (2012), 335-342.
57. A.
Fonda, M. Sabatini and F. Zanolin,
Periodic solutions of perturbed
Hamiltonian systems in the plane by the use of the Poincaré-Birkhoff
Theorem,
Topological Methods in
Nonlinear Analysis 40 (2012), 29-52.
58. A.
Fonda and A. Sfecci,
Periodic solutions of a system
of coupled oscillators with one-sided superlinear retraction forces,
Differential and Integral
Equations 25 (2012), 993-1010 (contact
me for more information).
59. A.
Fonda and M. Garrione,
A Landesman-Lazer type
condition for asymptotically linear second order equations with a
singularity,
Proceedings of the Royal
Society of Edinburgh 142 (2012), 1263-1277.
60. A.
Fonda and A. Sfecci,
Periodic bouncing solutions for
nonlinear impact oscillators,
Advanced Nonlinear Studies 13
(2013), 179-189.
61. A.
Fonda,
On a geometrical formula
involving medians and bimedians,
Mathematics Magazine 86 (2013),
351-357.
62. A.
Fonda and M. Garrione,
Generalized Sturm-Liouville
boundary conditions for first order differential systems in the plane,
Topological Methods in
Nonlinear Analysis 42 (2013), 293-325.
63. A.
Fonda,
Existence and uniqueness of
solutions for semilinear equations involving anti-selfadjoint operators,
Potugaliae Mathematica 71
(2014), 183-192.
64. A.
Fonda and P. Gidoni,
A permanence theorem for local
dynamical systems,
Nonlinear Analysis,
Theory, Methods and Applications 121 (2015), 73-81.
65. A.
Fonda and A. J. Ureña,
A higher-dimensional
Poincaré-Birkhoff theorem without monotone twist,
Comptes
Rendus Mathématique, Académie des Sciences de Paris, Série I 354 (2016),
475-479.
66. A.
Fonda and A. Sfecci,
Periodic solutions of weakly
coupled superlinear systems,
Journal of Differential
Equations 260 (2016), 2150-2162.
67. A.
Fonda and P. Gidoni,
Generalizing the
Poincaré-Miranda theorem: the avoiding cones condition,
Annali di Matematica Pura ed
Applicata 195 (2016), 1347-1371.
68. A.
Fonda, M. Garrione and P. Gidoni,
Periodic perturbations of
Hamiltonian systems,
Advances in Nonlinear Analysis
5 (2016), 367–382.
69. A.
Fonda and A.J. Ureña,
A
higher dimensional Poincaré-Birkhoff theorem for Hamiltonian
flows,
Annales
de l'Institut H. Poincaré, Analyse non lineaire 34 (2017), 679-698.
70. A.
Fonda and A. Sfecci,
On a singular periodic
Ambrosetti-Prodi problem,
Nonlinear
Analysis, Theory, Methods and Applications 149 (2017), 146-155.
71. A.
Fonda and P. Gidoni,
An avoiding cones condition for
the Poincaré-Birkhoff Theorem,
Journal
of Differential Equations 262 (2017), 1064-1084.
72.
A. Fonda and A.
Sfecci,
Multiple
periodic solutions of Hamiltonian systems confined in a box,
Discrete
and Continuous Dynamical Systems 37 (2017), 297-301.
73. A.
Fonda and A.C. Gallo,
Periodic
perturbations of the Kepler problem,
Celestial
Mechanics and Dynamical Astronomy 129 (2017), 257-268.
74. A.
Fonda and A.C. Gallo,
Periodic
perturbations with rotational symmetry of planar systems driven by a
central force,
Journal
of Differential Equations 264 (2018), 7055-7068.
75. A.
Fonda,
Generalizing the
Lusternik-Schnirelmann critical point theorem,
Bulletin
of the London Mathematical Society 51 (2019), 25-33.
76.
A. Fonda,
A generalization of the
parallelogram law to higher dimensions,
Ars
Mathematica Contemporanea 16 (2019), 411-417.
77. A.
Fonda and R. Toader,
Subharmonic solutions
of Hamiltonian systems displaying some kind of sublinear growth,
Advances
in Nonlinear Analysis 8 (2019), 583-602.
78.
A. Fonda and
A.J. Ureña,
A Poincaré-Birkhoff theorem for
Hamiltonian flows on nonconvex domains,
Journal
de Mathématiques Pures et Appliquées 129 (2019), 131-152.
79. A.
Fonda and G. Klun,
On the topological degree of
planar maps avoiding normal cones,
Topological
Methods in Nonlinear Analysis 53 (2019), 825-845.
80. A.
Boscaggin, A. Fonda and M. Garrione,
An infinite-dimensional
version of the Poincaré-Birkhoff theorem on the Hilbert cube,
Annali
della Scuola Normale di Pisa 20 (2020), 751-770.
81. A.
Fonda, J. Mawhin and M. Willem,
Multiple periodic solutions of
infinite-dimensional pendulum-like equations,
Pure
and Applied Functional Analysis 5 (2020), 951-963.
82.
A. Fonda and P. Gidoni,
Coupling linearity and twist: an
extension of the Poincaré-Birkhoff Theorem for Hamiltonian systems,
NoDEA
- Nonlinear Differential Equations and Applications,
27 (2020), Paper No. 55, 26 pp.
83.
A. Fonda, G. Klun and A. Sfecci,
Periodic solutions of nearly
integrable Hamiltonian systems bifurcating from infinite-dimensional tori,
Nonlinear
Analysis, Theory, Methods and Applications 201
(2020), Paper No. 111720, 16 pp.
84. A.
Fonda and R. Toader,
A dynamical approach to lower and
upper solutions for planar systems,
Discrete
and Continuous Dynamical Systems 41 (2021), 3683-3708.
85. A.
Fonda, G. Klun and A. Sfecci,
Well-ordered and non-well-ordered
lower and upper solutions for periodic planar systems,
Advanced
Nonlinear Studies 21 (2021), 397-419.
86. A.
Fonda, G. Klun and A. Sfecci,
Periodic solutions of second
order differential equations in Hilbert spaces,
Mediterranean
Journal of Mathematics 18 (2021), Paper No. 223, 26 pp.
87. A.
Fonda and R. Toader,
Subharmonic solutions of weakly
coupled Hamiltonian systems,
Journal
of Dynamics and Differential Equations (2021), DOI:
10.1007/s10884-021-10106-1.
88. C.
Fabry and A. Fonda,
A systematic approach to
nonresonance conditions for periodically forced planar Hamiltonian systems,
Annali
di Matematica Pura ed Applicata 201 (2022), 1033-1074.
89. A.
Fonda, G. Klun and A. Sfecci,
Non-well-ordered lower and upper
solutions for semilinear systems of PDEs,
Communications
in Contemporary Mathematics 24 (2022), Paper No. 2150080, 20 pp.
90. A.Fonda,
A. Sfecci and R. Toader,
Two-point boundary value problems
for planar systems: a lower and upper solutions approach,
Journal
of Differential Equations 308 (2022), 507-544.
91. A.
Fonda, G. Klun, F. Obersnel and A. Sfecci,
On the Dirichlet problem
associated to bounded perturbations of positively-(p, q)-homogeneous
Hamiltonian systems,
Journal
of Fixed Point Theory and Applications 24
(2022), Paper No. 66, 32
pp.
92. A.
Fonda, G. Klun and A. Sfecci,
On Dini derivatives of real
functions,
Publicationes Mathematicae
Debrecen 102 (2023), 33-43.
Preprints:
1. A.
Fonda,
A logarithmic spiral in the
complex plane interpolating between the exponential and the circular
functions,
Preprint
2018
2. A. Fonda,
M. Garzón and A. Sfecci,
An extension of the
Poincaré–Birkhoff Theorem coupling twist with lower and upper solutions,
Preprint
2022.
3. A.
Fonda, N.G. Mamo, F. Obersnel and A. Sfecci,
A lower/upper solutions result
for generalised radial p-Laplacial boundary value problems,
Mediterranean
Journal of Mathematics, to appear.
4. A. Fonda and W.
Ullah,
Periodic solutions of Hamiltonian
systems coupling twist with generalized lower/upper solutions,
Preprint
2022.
5. A. Fonda and
P.J. Torres,
Periodic solutions of
discontinuous second order differential equations. The porpoising effect,
Preprint
2022.
6. A. Fonda and R.
Ortega,
A two-point boundary value
problem associated with Hamiltonian systems on a cylinder,
Rendiconti
del Circolo Matematico di Palermo, to appear.
As an Editor:
1. Handbook of Differential Equations: Ordinary Differential Equations (vol. 1, 2, 3),
A. Canada, P. Drabek and A. Fonda Eds, Elsevier, Amsterdam, 2004-2006.
Textbooks:
1. A. Fonda, Lezioni sulla teoria dell'integrale, Ed. Goliardiche, Roma, 2001.
2. A. Fonda, Playing around resonance. An invitation to the search of periodic solutions for second order ordinary differential equations, Birkhauser/Springer, 2016 (contact me for more information). See here a list of Errata.
3. A. Fonda, The
Kurzweil-Henstock
integral for undergraduates. A promenade along the
marvelous theory of integration, Birkhauser/Springer,
2018 (contact
me for more information). See here a list of Errata.