@conference{
	11589_20518,
	author = { Caponio E  and  Devillanova G  and  Maddalena F  and  Masiello A  and  Solimini S },
	title = {Problems in Calculus of Variations and Nonlinear Analysis},
	year = {2014},
	publisher = {Cangemi Editore},
	booktitle = {Proceedings of the ``1st Workshop on the State of the Art and Challenges of Research Efforts at POLIBA,  03--05 dicembre 2014, Bari, Italy},
	pages = {227--331}
}
@article{
	11589_52324,
	author = { Caponio E  and  Javaloyes M A  and  Masiello A },
	title = {Addendum to "Morse theory of causal geodesics in a stationary spacetime via Morse theory of geodesics of a Finsler metric", Ann. Inst. H. Poincaré Anal. Non  Linéaire, 27 (2010) 857--876},
	year = {2013},
	journal = {ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE},
	volume = {30},
	abstract = {We give the details of the proof of the existence of an isomorphism between some homological groups related to the critical groups of the energy functional of a Finsler manifold in the two end-points boundary conditions.},
	keywords = {Morse theory, critical groups, Finsler metric},
	doi = {10.1016/j.anihpc.2013.03.005},	
	pages = {961--968}
}
@article{
	11589_52081,
	author = { Caponio E  and  Javaloyes MA  and  Masiello A },
	title = {On the energy functional on Finsler manifolds and applications to stationary spacetimes},
	year = {2011},
	journal = {MATHEMATISCHE ANNALEN},
	volume = {351},
	abstract = {In this paper, we first study some global properties of the energy
functional on a non-reversible Finsler manifold. In particular we
present a fully detailed proof of the Palais--Smale condition under
the completeness of the Finsler metric. Moreover we define a Finsler
metric of Randers type, which we call Fermat metric, associated to a
conformally standard stationary spacetime. We shall study the
influence of the Fermat metric  on the causal properties of the
spacetime, mainly the global hyperbolicity. Moreover we study the
relations between the energy functional of the Fermat metric and the
Fermat principle for the light rays in the spacetime.
This allows one to obtain existence and multiplicity results for light
rays, using the Finsler theory. Finally the case of timelike
geodesics with fixed energy is considered.
The research that led to the present paper was partially supported  
by a grant of the group GNAMPA of INdAM},
	keywords = {Finsler metric, critical point theory, causality, geodesics},
	doi = {10.1007/s00208-010-0602-7},	
	pages = {365--392}
}
@article{
	11589_2008,
	author = { Caponio E  and  Javaloyes MA  and  Masiello A },
	title = {Morse theory of causal geodesics in a stationary spacetime via Morse theory of geodesics of a Finsler metric},
	year = {2010},
	journal = {ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE},
	volume = {27},
	abstract = {We show that the index of a lightlike geodesic in a conformally standard stationary spacetime  is equal to the index of its spatial projection as a geodesic of a Finsler metric. Moreover we obtain the Morse relations of lightlike geodesics connecting a point  to a curve  by using Morse theory on the Finsler manifold. To this end, we prove a splitting lemma for the energy functional of a Finsler metric. Finally, we show that the reduction to Morse theory of a Finsler manifold can be done also for timelike geodesics.},
	keywords = {Morse theory; Finsler metric; Index theorem},
	doi = {10.1016/j.anihpc.2010.01.001},	
	pages = {857--876}
}
@article{
	11589_6389,
	author = { Caponio E  and  Javaloyes MA  and  Masiello A },
	title = {Finsler geodesics in the presence of a convex function and their applications},
	year = {2010},
	journal = {JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL},
	volume = {43},
	abstract = {In this paper, we obtain a result about the existence of only a finite number of geodesics between two fixed non-conjugate points in a Finsler manifold endowed with a convex function. We apply it to Randers and Zermelo metrics. As a by-product, we also get a result about the finiteness of the number of lightlike and timelike geodesics connecting an event to a line in a standard stationary spacetime.},
	keywords = {convexity; Finsler metric; geodesic},
	doi = {10.1088/1751-8113/43/13/135207},	
}
@article{
	11589_5335,
	author = { Javaloyes  M A  and  Masiello  A  and  Piccione  P },
	title = {Pseudo focal points along Lorentzian geodesics and Morse index},
	year = {2010},
	journal = {ADVANCED NONLINEAR STUDIES},
	volume = {10},
	keywords = {Geodesies; Lorentzian manifolds; Morse index theorem},
	pages = {53--82}
}
@article{
	11589_2204,
	author = { Giambò  R  and  Giannoni  F  and  Masiello  A },
	title = {Functional regularity properties for light rays in general relativity},
	year = {2009},
	journal = {JOURNAL OF MATHEMATICAL PHYSICS},
	volume = {50},
	abstract = {In this note we consider some functionals restricted to the nonholonomic constraint satisfied by lightlike curves in Lorentzian manifolds. These functionals are related to the arrival time map, whose critical points are light rays in general relativity, and they have been used in the variational theory of light rays in some recent literatures. We exhibit an explicit example showing that, from a functional point of view, the constraint above does not have sufficient regularity. Nevertheless, we show that up to a continuous change in coordinates, the used functionals restricted to the constraint have just the regularity that one needs to develop Lusternik-Schnirelmann theory or Morse theory.},
	doi = {10.1063/1.3158853},	
}
@article{
	11589_9359,
	author = { Masiello A},
	title = {An alternative variational principle for geodesics of a Randers metric},
	year = {2009},
	journal = {ADVANCED NONLINEAR STUDIES},
	volume = {9},
	pages = {783--801}
}
@conference{
	11589_20856,
	author = { MASIELLO A},
	title = {Variational properties of the relativistic Lorentz force equation},
	year = {2006},
	booktitle = {Recent Developments in Gravitational Physics},
	pages = {171--180}
}
@conference{
	11589_14395,
	author = { MASIELLO A},
	title = {Some variational problems in semi-Riemannian geometry},
	year = {2006},
	publisher = {SPRINGER},
	address = {HEIDELBERG},
	journal = {LECTURE NOTES IN PHYSICS},
	volume = {692},
	booktitle = {Analytical and Numerical Approaches to Mathematical Relativity},
	doi = {10.1007/b11550259},	
	pages = {51--77}
}
@article{
	11589_9046,
	author = { MASIELLO A},
	title = {On the Geodesic Connectedeness of a Class of Lorentzian Manifolds with Boundary},
	year = {2006},
	journal = {ADVANCED NONLINEAR STUDIES},
	volume = {6},
	pages = {287--308}
}
@misc{
	11589_24544,
	author = { BENCI V  and  MASIELLO A },
	title = {NONLINEAR ANALYSIS AND APPLICATIONS TO PHYSICAL SCIENCES},
	year = {2004},
	publisher = {Springer-Verlag Italia},
	address = {MILANO}
}
@article{
	11589_629,
	author = { MASIELLO A  and  PICCIONE P },
	title = {On the number of solutions for the two-point  value problem on Riemannian manifolds},
	year = {2004},
	journal = {JOURNAL OF GEOMETRY AND PHYSICS},
	volume = {49},
	doi = {10.1016/S0393-0440(03)00070-6},	
	pages = {67--88}
}
@article{
	11589_8840,
	author = { Caponio E  and  Masiello A  and  Piccione P },
	title = {Maslov index and Morse theory for the relativistic Lorentz force equation},
	year = {2004},
	journal = {MANUSCRIPTA MATHEMATICA},
	volume = {113},
	abstract = {We study the Jacobi equation for fixed endpoints solutions of the Lorentz force equation on a Lorentzian manifold. The flow of the Jacobi equation along each solution preserves the so-called twisted symplectic form, and the corresponding curve in the symplectic group determines an integer valued homology class called the Maslov index of the solution. We introduce the notion of F-conjugate plane for each conjugate instant; the restriction of the spacetime metric to the F-conjugate plane is used to compute the Maslov index, which is given by a sort of algebraic count of the conjugate instants. For a stationary Lorentzian manifold and an exact electromagnetic field admitting a potential vector field preserving the flow of the Killing vector field, we introduce a constrained action functional having finite Morse index and whose critical points are fixed endpoints solution of the Lorentz force equation. We prove that the value of this Morse index equals the Maslov index and we prove the Morse relations for the solutions of the Lorentz force equation in a static spacetime.},
	keywords = {Maslov index; Morse theory; Lorentz force law},
	doi = {10.1007/s00229-004-0441-5},	
	pages = {471--506}
}
@article{
	11589_9229,
	author = { MASIELLO A  and  CAPONIO E  and  PICCIONE P },
	title = {Maslov Index and Morse Theory for  the relativistic Lorentz force equation},
	year = {2004},
	journal = {MANUSCRIPTA MATHEMATICA},
	volume = {113},
	doi = {10.1007/s00229-004-0441-5},	
	pages = {471--506}
}
@article{
	11589_9237,
	author = { MASIELLO A  and  CAPONIO E },
	title = {Causal properties of Kaluza--Klein metrics},
	year = {2004},
	journal = {APPLIED MATHEMATICS LETTERS},
	volume = {17},
	doi = {10.1016/j.aml.2004.01.004},	
	pages = {1371--1374}
}
@article{
	11589_8839,
	author = { Caponio E  and  Masiello A },
	title = {The Avez-Seifert theorem for the relativistic Lorentz force equation},
	year = {2004},
	journal = {JOURNAL OF MATHEMATICAL PHYSICS},
	volume = {45},
	abstract = {In this paper we prove an extension of the Avez-Seifert theorem to the relativistic Lorentz force equation. Let (M,g) be a globally hyperbolic space-time, F an exact 2-form on M representing the electromagnetic field, (F) over cap the Lorentz force associated to F, and q a charge for a test particle. Let p(0) and p(1) be two chronologically related points on M, then there exists a future-pointing timelike solution of the Lorentz force equation D-s(z)over dot=q (F) over cap (z)[(z)over dot], connecting p(0) and p(1). (C) 2004 American Institute of Physics.},
	keywords = {Kaluza-Klein; globally hyperbolic spacetime; Lorentz force law},
	doi = {10.1063/1.1782673},	
	pages = {4134--4140}
}
@article{
	11589_9193,
	author = { MASIELLO A  and  CAPONIO E },
	title = {The Avez--Seifert Theorem for the relativistic Lorentz force equation},
	year = {2004},
	journal = {JOURNAL OF MATHEMATICAL PHYSICS},
	volume = {45},
	doi = {10.1063/1.1782673},	
	pages = {4134--4140}
}
@conference{
	11589_13695,
	author = { MASIELLO A},
	title = {Geodesics on Lorentzian manifolds: a 
variational approach},
	year = {2003},
	volume = {Publication de la RSME n. 5},
	pages = {183--203}
}
@article{
	11589_10349,
	author = { MASIELLO A  and  ABBONDANDOLO A  and  BENCI V  and  FORTUNATO D },
	title = {On the Morse inequalities for geodesics on Lorentzian manifolds},
	year = {2003},
	journal = {MATHEMATICAL RESEARCH LETTERS},
	volume = {10},
	pages = {435--445}
}