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,
           M
ultiple 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, 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), 111720.

83. 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, online first, DOI: 10.1007/s00030-020-00653-9.

Preprints:

1. A. Fonda,
           A logarithmic spiral in the complex plane interpolating between  the exponential and the circular functions,
          
Preprint 2018.

2. A. Fonda and R. Toader,
           Subharmonic solutions of weakly coupled Hamiltonian systems,
          
Preprint 2019.

3. C. Fabry and A. Fonda,
           A systematic approach to nonresonance conditions for periodically forced planar Hamiltonian systems,
          
Preprint 2020.

4. A. Fonda, G. Klun and A. Sfecci,
           Periodic solutions of second order differential equations in Hilbert spaces,
          
Preprint 2020.

5. A. Fonda, G. Klun and A. Sfecci,
           Non-well-ordered lower and upper solutions for semilinear systems of PDEs,
          
Preprint 2020.

6. A. Fonda and R. Toader,
           A dynamical approach to lower and upper solutions for planar systems,
          
Preprint 2020.

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).

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.