Mathematics

 Research

In my research, under the supervision of Prof. Fabio Zanolin, I deal with boundary value problems associated with second order nonlinear equations. The aim of my studies is to achieve existence and multiplicity results for positive solutions. As first step, I consider equations of the form u’’ + c u’ + a(x) g(u) = 0, where a(x) is an indefinite (i.e. sign-changing) weight function and g(s) satisfies suitable growth conditions at zero and at infinity. Using topological techniques I treat Dirichlet, Neumann, and periodic boundary value problems and consider different growth conditions on the nonlinear function g(s) . Moreover, the method provides a topological approach to detect infinitely many subharmonic solutions, to study globally defined positive solutions with complex behavior and to deal with chaotic dynamics. Furthermore, this innovative technique has the potential and the generality needed to deal with indefinite problems with more general differential operators, as in the case of problems involving PDEs.

Education

• 2010-2012: Master Degree
  University of Udine
  Advisor: Prof. Fabio Zanolin
  Thesis: Fixed point index, Krasnosel'skii theorems and existence of positive solutions
  110/110 cum Laude

• 2007-2010: Bachelor Degree
  University of Udine
  Advisor: Prof. Stefano Ansoldi
  Thesis: The mathematical foundations of the electromagnetic theory
  110/110 cum Laude 

Publications

• G. Feltrin, F. Zanolin, Multiple positive solutions for a superlinear problem: a topological approach, J. Differential Equations 259 (2015), 925–963. (link) (arxiv) (SDL)
• G. Feltrin, F. Zanolin, Existence of positive solutions in the superlinear case via coincidence degree: the Neumann and the periodic boundary value problems, Adv. Differential Equations 20 (2015), 937–982. (link) (arXiv) (SDL)
• G. Feltrin, Existence of positive solutions of a superlinear boundary value problem with indefinite weight, Discrete Contin. Dyn. Syst. 2015, Dynamical systems, differential equations and applications. 10th AIMS Conference. Suppl., 436–445. (link) (arXiv) (SDL)
• A. Boscaggin, G. Feltrin, F. Zanolin, Pairs of positive periodic solutions of nonlinear ODEs with indefinite weight: a topological degree approach for the super-sublinear case, Proc. Roy. Soc. Edinburgh Sect. A 146 (2016), 449–474. (link) (arXiv) (SDL)
• A. Boscaggin, G. Feltrin, F. Zanolin, Positive solutions for super-sublinear indefinite problems: high multiplicity results via coincidence degree, Trans. Amer. Math. Soc., to appear. (link) (arXiv) (SDL) 

Preprints

• G. Feltrin, A note on a fixed point theorem on topological cylinders, preprint. (link) (SDL)
• G. Feltrin, F. Zanolin, Multiplicity of positive periodic solutions in the superlinear indefinite case via coincidence degree, preprint. (link)
• A. Boscaggin, G. Feltrin, Positive subharmonic solutions to nonlinear ODEs with indefinite weight, preprint. (link) (SDL)
• G. Feltrin, Multiple positive solutions of a Sturm-Liouville boundary value problem with conflicting nonlinearities, preprint. (link)
• G. Feltrin, F. Zanolin, An application of coincidence degree theory to cyclic feedback type systems associated with nonlinear differential operators, preprint. (link)

Ph.D. thesis

• G. Feltrin, Positive solutions to indefinite problems: a topological approach. (SDL)

ORCID - Guglielmo Feltrin MathSciNet - Guglielmo Feltrin Scopus - Guglielmo Feltrin zbMATH - Guglielmo Feltrin Google Scholar - Guglielmo Feltrin ResearchGate - Guglielmo Feltrin Mathematics Genealogy Project

(Last updated: 2016-09-30)