Curriculum

Gabriele Bonanno is Full Professor of Mathematical Analysis at the University of Messina. In the past, he was Researcher first, and Associate Professor then, in Mathematical Analysis at the University of Reggio Calabria in the period 1992-2006. He was graduated with laude in Mathematics at the University of Messina in 1988 and he was research grant winner for senior students in Mathematics from CNR in 1987. He is author of more than one hundred scientific papers published in international journals widely circulated as Nonlinear Analysis, Journal of Mathematical Analysis and Applications, Journal of Differential Equations, Nonlinear Differential Equations and Applications, etc.... He has collaborated with more than 30 co-authors including 13 foreign researchers.
The research topics of such publications are in the following fields: 1) Ordinary Differential Equations, 2) Elliptic Partial Differential Equations, 3) Set-Valued Analysis and Applications, 4) Theory of Global Optimization, 5) Variational Methods. In the first field, higher order ordinary differential equations, fourth order ordinary differential equations, and singular second order boundary value problems have been studied, establishing existence results and, in some case, uniqueness, or multiplicity results. Implicit equations of first and second order have also been investigated. The approaches are based on fixed point theorems, variational methods, and set-valued analysis techniques. In the second field, Dirichlet problems in bounded or unbounded domains have been studied, by establishing the existence of strong or weak solutions. In particular, the case with discontinuous terms has been treated under various points of view and by using several methods, such as fixed point theorems for weakly sequentially continuous maps, fixed point theorems for monotone operators, set-valued techniques and variational methods in the framework of the non-smooth analysis. Further results concerning implicit elliptic equations have been obtained. In the third field, the following topics have been studied: Carathéodory selections, Scorza Dragoni property, random differential inclusions, first order ordinary differential inclusions, second order ordinary differential inclusions, elliptic differential inclusions, fixed point theorems. In the fourth field, a suitable class of functionals, defined on decomposable spaces of measurable functions, which has the property that the local minima are also global, has been introduced. Moreover, he pointed out that integral functional belongs to such a class. In the fifth field, some theorems which giving the existence of three critical points for differentiable functionals have been obtained. This study is also based on an appropriate minimax inequality, for which a suitable characterization has been given. A local minimum theorem has been pointed out and, among the consequences, a two non-zero critical points theorem has been presented and an infinitely many critical points result has been highlighted. It was given a characterization of the mountain pass geometry, that is one of the key assumptions of the classical and powerful Ambrosetti-Rabinowitz theorem, and a version of the mountain pass theorem for a suitable class of functionals has been established by requiring a type of Palais-Smale condition weaker than the classical one. Such results have been applied to obtain multiple solutions (that is two, three or infinitely many solutions) to nonlinear differential problems, as, for instance, Neumann or Dirichlet problems for elliptic equations involving the p-Laplacian, possibly also with variable exponent.
Gabriele Bonanno held more than fifty talks, including conferences and communications. In particular, he was invited abroad, as keynote speaker or main speaker, in several countries such as the United States, Portugal, Greece, Romania, Spain, Czech Republic, Germany, etc.... He was in several scientific committee of congresses and workshops (for instance in Messina and Palermo) or special sessions in international congresses (for instance in the United States, Czech Republic and Spain). Moreover, he was appointed by the President of UMI ("Unione Matematica Italiana") as Coordinator, together with A. Sorrentino, of the Section entitled "Ordinary Differential Equations and Dynamical Systems" at the next UMI Congress to be held in Pavia in September 2019.
He works and has served as an editor in many journals, as Nonlinear Analysis (Real World and Applications), Open mathematics (formerly Central European Journal of Mathematics), Electronic Journal of Qualitative Theory of Differential Equations. He is a referee for many mathematics journals by evaluating many hundreds of scientific articles. He is an ordinary member of the "Peloritana dei Pericolanti" Academy.
Gabriele Bonanno is the principal investigator of the project PRIN 2017 “Nonlinear Differential Problems via Variational, Topological and Set-valued Methods” (Prot. 2017AYM8XW  D.D. MIUR 14/02/2019) funded with  Euro 252.556 and he was the local principal investigator of the Team of Messina University of PRIN 2007 "Ordinary Differential Equations and Applications" (National Principal Investigator: Fabio Zanolin) and, again, he was the local principal investigator of the Team of Messina University of PRIN 2009 "Ordinary Differential Equations and Applications" (National Principal Investigator: Fabio Zanolin) , which have been both funded. Moreover, he was principal investigator of Research Programmes RdB (ex 60%) and PRA (ex 60%) of Mathematical Analysis at the Reggio Calabria (2001, 2002, 2003-04, 2005) and Messina (2006-07, 2008-09) universities, all funded. These projects have been on research topics as ordinary and partial differential equations, variational methods, set-valued analysis.
“Scientific awards and bibliometric data.”
Gabriele Bonanno received by the Journal of Differential Equations the acknowledgment for the most cited article. Specifically, the article "Bonanno G., Candito P., Non-differentiable functionals and applications to elliptic problems with discontinuous nonlinearities, Journal of Differential Equations 244 (2008), 3031-3059" was the most cited article in the journal during the five years 2008-2012. Gabriele Bonanno received by Applicable Analysis the acknowledgment that article "Bonanno G., Marano S.A., On the structure of the critical set of non-differentiable functions with a weak compactness condition, Applicable Analysis, 89 (2010), 1-10" was among the most cited in 2011. The following three articles submitted by Gabriele Bonanno for the evaluation of research (VQR 2004-2010) have obtained the highest rating, i.e. 1 + 1 + 1, having been judged all excellent: "Bonanno G., Candito P., Non-differentiable functionals and applications to elliptic problems with discontinuous nonlinearities, Journal of Differential Equations 244 (2008), 3031-3059”, "Bonanno G., Livrea R., Multiple periodic solutions for Hamiltonian systems with not coercive potential, Journal of Mathematical Analysis and Applications, 363 (2010), 627-638" e "Bonanno G., Molica Bisci G., Infinitely many solutions for a Dirichlet problem involving the p-Laplacian. Proceedings of the Royal Society of Edinburgh Section A Mathematics, 140 (2010), 737-752". Moreover, the two articles submitted for the evaluation of research (VQR 2011-2014): “Bonanno G., A critical point theorem via the Ekeland variational principle, Nonlinear Analysis, 75 (2012), 2992-3007” and “Bonanno G., Chinnì A., Discontinuous elliptic problems involving the p(x)-laplacian,, Mathematische Nachrichten 284 (2011), 639-652” have respectively obtained rating 1 and 0.7.
114 of his publications have been reviewed by MathSciNet to date (more recent articles will be reviewed later) by reporting 1.707 citations in total, with 23 h-index. 93 of his publications have been reviewed by Web of Sience to date (more recent articles will be reviewed later) by reporting 1.865 citations in total, with 25 h-index. 96 of his publications have been reviewed by Scopus to date (more recent articles will be reviewed later) by reporting 2.027 citations in total, with 26 h-index. Moreover, 5 among his articles appear in Web of Science as "Highly Cited Paper". Finally, from the data provided by the publisher Elsevier (Top 25 hottest Articles) it follows that the following articles were among the most downloaded in the period of their publication. Precisely:
8th place from April to June 2008: Journal of Differential Equations 244 (2008), 3031-3059. 16th place from April to June 2008: Journal of Mathematical Analysis and Applications 343 (2008), 1166-1176. 15th place from January to March 2009: Applied Mathematics and Computations 208 (2009), 318-327. 10th place from April to June 2009: Journal of Mathematical Analysis and Applications 358 (2009), 223-228. 15th place from July to September 2009: Journal of Mathematical Analysis and Applications 358 (2009), 223-228. 6th place from April to June 2010 Applied Mathematics Letter, 23 (2010), 807-811. 11th place from January to March 2011: Comptes Rendus Mathématique, Académie des Sciences, Paris, 349 (2011), 263-268. 2th place from Aprile to June 2011: Journal Mathematical Analysis and Application, 382 (2011), 1-8. 14th place from July to September 2011: Comptes Rendus Mathématique, Académie des Sciences, Paris, 349 (2011), 263-268. 21th place October to December 2011: Comptes Rendus Mathématique, Académie des Sciences, Paris, 349 (2011), 263-268. 19th place from January to December 2011(full year): Journal Mathematical Analysis and Application, 382 (2011), 1-8. 6th place from January to December 2011(full year): Comptes Rendus Mathématique, Académie des Sciences, Paris, 349 (2011), 263-268. 5th place from January to March 2012: Journal of Mathematical Analysis and Application, 390 (2012), 59-67. 10th place from January to March 2012: Comptes Rendus Mathématique, Académie des Sciences, Paris, 350 (2012), 187-191. 5th place from January to March 2012: Nonlinear Analysis, 75 (2012), 2992-3007.