@article{
	11589_6688,
	author = { Bartolo R  and  Candela AM  and  Flores JL },
	title = {Connection by geodesics on globally hyperbolic spacetimes 
with a lightlike Killing vector field},
	year = {9999},
	journal = {REVISTA MATEMATICA IBEROAMERICANA},
	abstract = {Given a globally hyperbolic spacetime endowed
with a complete lightlike Killing vector field and a complete
Cauchy hypersurface, we characterize the points which can be
connected by geodesics. A straightforward consequence is the
geodesic connectedness of globally hyperbolic generalized plane
waves with a complete Cauchy hypersurface.},
	keywords = {Lightlike vector field, global hyperbolicity, geodesic connectedness, Killing vector field, Cauchy hypersurface, stationary spacetime, gravitational wave, generalized plane wave.}
}
@article{
	11589_3179,
	author = { Bartolo R  and  Fiscella A },
	title = {Multiple solutions for a class of Schroedinger equations
involving the fractional p–Laplacian},
	year = {9999},
	journal = {MINIMAX THEORY AND ITS APPLICATIONS}
}
@article{
	11589_81863,
	author = { Bartolo  R  and  Molica Bisci  G },
	title = {Asymptotically linear fractional p-Laplacian equations},
	year = {2016},
	journal = {ANNALI DI MATEMATICA PURA ED APPLICATA},
	doi = {10.1007/s10231-016-0579-2},	
}
@article{
	11589_81864,
	author = { Bartolo  R  and  De Nàpoli  P  and  Salvatore  A },
	title = {Infinitely many solutions for non--local problems with broken symmetry},
	year = {2016},
	journal = {ADVANCES IN NONLINEAR ANALYSIS},
	doi = {10.1515/anona-2016-0106},	
}
@article{
	11589_60330,
	author = { Bartolo R. and  Candela A.M. and  Salvatore A.},
	title = {On a class of superlinear (p,q)-Laplacian type equations on R^N},
	year = {2016},
	journal = {JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS},
	volume = {438}
}
@article{
	11589_6692,
	author = { Bartolo R  and  Candela AM  and  Salvatore A },
	title = {Multiplicity results for a class of asymptotically p-linear equations on R^N},
	year = {2016},
	journal = {COMMUNICATIONS IN CONTEMPORARY MATHEMATICS},
	volume = {18},
	abstract = {The aim of this paper is investigating the multiplicity of weak solutions of the quasilinear elliptic equation
\[
-\Delta_p u + V(x)|u|^{p-2}u\ =\ g(x, u), \quad x \in\R^N,
\]
where $1<p<+\infty$, $\Delta_p u= {\rm div}(|\nabla u|^{p-2}\nabla u)$, the nonlinearity $g$ behaves as 
$|u|^{p-2}u$ at infinity and $V$ is a potential satisfying the assumptions in \cite{bf}, so that a 
suitable embedding theorem for weighted Sobolev spaces holds. Both the non--resonant and the resonant case are analyzed.},
	keywords = {Asymptotically $p$--linear problem, $p$--Laplacian operator,  Schr\"odinger equation,   unbounded domain, variational methods, weighted Sobolev space, compact embedding, pseudo--genus, resonant problem.},
	doi = {DOI: 10.1142/S0219199715500315},	
}
@article{
	11589_6063,
	author = { Bartolo R  and  A M  Candela  and  J L  Flores },
	title = {CONNECTION BY GEODESICS ON OPEN SUBSETS OF GLOBALLY HYPERBOLIC SPACETIMES},
	year = {2015},
	journal = {INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS},
	volume = {12},
	doi = {DOI: 10.1142/S0219887815600099},	
}
@article{
	11589_6925,
	author = { Bartolo R  and  A M  Candela  and  A  Salvatore },
	title = {Infinitely many solutions
 for a perturbed Schroedinger equation},
	year = {2015},
	journal = {DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS},
	volume = {Suppl.},
	doi = {doi:10.3934/proc.2015.0094},	
	pages = {94--102}
}
@article{
	11589_8119,
	author = { Bartolo R  and  G  Molica Bisci },
	title = {A pseudo--index approach to fractional equations},
	year = {2015},
	journal = {EXPOSITIONES MATHEMATICAE},
	volume = {33},
	abstract = {The aim of this paper is investigating the existence of weak solutions to non--local equations involving a general integro--differential operator of fractional type, when the nonlinearity is subcritical and asymptotically linear at infinity. These equations admit a variational structure and, in presence of an odd symmetric nonlinearity, we  prove multiplicity results by using a pseudo--index theory related to the genus. As a particular case we derive existence and multiplicity results for non--local equations involving the fractional Laplacian operator.},
	keywords = {Fractional Laplacian; integro–differential operator; variational methods},
	doi = {doi:10.1016/j.exmath.2014.12.001},	
	pages = {502--516}
}
@conference{
	11589_60293,
	author = { Bartolo  Rossella  and  Capozzi  Alberto  and  Cerami  Giovanna  and  Cingolani  Silvia  and  D’Avenia  Pietro  and  Greco  Carlo  and  Palagachev  Dian  and  Pomponio  Alessio  and  Vannella  Giuseppina },
	title = {Variational methods in the study of nonlinear problems and applications},
	year = {2014},
	publisher = {Gangemi Editore spa},
	address = {Roma},
	volume = {B},
	booktitle = {I gruppi di ricerca sfide tecnologiche e sociali},
	abstract = {In this paper we illustrate the lineguides of our research group. We describe some 
recent results concerning the study of some nonlinear differential equations and systems 
having a variational nature and arising from physics, geometry and applied sciences. In 
particular we report existence, multiplicity and regularity results for the solutions of these 
nonlinear problems. We point out that, in treating the above problems, the used methods for 
finding solutions are variational and topological, indeed the existence of solutions of the 
considered equations is obtained searching for critical points of suitable functionals defined on 
manifolds embedded into infinite dimensional functional spaces, while the regularity of the 
solutions is studied by means of geometric and harmonic analysis tools.},
	keywords = {Nonlinear Partial Differential Equations, Solutions, Existence, Multiplicity, Regularity},
	pages = {179--183}
}
@article{
	11589_6834,
	author = { Bartolo R},
	title = {Multiplicity results for a class of quasilinear elliptic problems},
	year = {2014},
	journal = {MEDITERRANEAN JOURNAL OF MATHEMATICS},
	volume = {11},
	abstract = {By using variational methods we prove the multiplicity of weak solutions of a class of asymptotically p-linear problems.},
	keywords = {Quasilinear elliptic equations; asymptotically p-linear problem; variational methods},
	doi = {DOI 10.1007/s00009-013-0378-6},	
	pages = {1099--1113}
}
@article{
	11589_8842,
	author = { BARTOLO R  and  CANDELA A M  and  SALVATORE A },
	title = {Perturbed asymptotically linear problems},
	year = {2014},
	journal = {ANNALI DI MATEMATICA PURA ED APPLICATA},
	volume = {193},
	abstract = {The aim of this paper is investigating the existence of solutions of the semilinear elliptic problem
\begin{equation}
\left\{
\begin{array}{ll}
\displaystyle{-\Delta u\ =\ p(x, u) + \varepsilon g(x, u)} 
& \mbox{ in }  \Omega,\\
 \displaystyle{u=0}  & \mbox{ on }  \partial\Omega,\\
 \end{array}
\right.
\end{equation}
where $\Omega$ is an open bounded domain of $\R^N$, $\varepsilon\in\R$, $p$ is subcritical and asymptotically linear at infinity and $g$ is just a continuous function. Even when this problem has not a variational structure on $H^1_0(\Omega)$, suitable procedures and estimates allow us to prove that the number of distinct crtitical levels of the functional associated to the unperturbed problem is ``stable'' under small perturbations, in particular obtaining multipicity results if $p$ is odd, both in the non--resonant and in the resonant case.},
	keywords = {Asymptotically linear elliptic problem, essential value, perturbed problem, variational methods, pseudo--genus, resonant problem.},
	doi = {10.1007/s10231-012-0267-9},	
	pages = {89--101}
}
@conference{
	11589_16610,
	author = { Bartolo R  and  Candela A M  and  Flores J L },
	title = {Global geodesic properties of Gödel type spacetimes},
	year = {2013},
	publisher = {Springer Science+Business Media New York 2012},
	address = {New York},
	volume = {26},
	booktitle = {Recent Trends in Lorentzian Geometry},
	abstract = {The aim of this paper is to review and complete the study of geodesics on
Gödel type spacetimes initiated in [8] and improved in [2]. In particular, we prove
some new results on geodesic connectedness and geodesic completeness for these
spacetimes.},
	keywords = {Gödel type spacetime, static spacetime, geodesic connectedness, geodesic completeness, variational principle.},
	doi = {DOI 10.1007/978-1-4614-4897-6 7},	
	pages = {179--193}
}
@conference{
	11589_21588,
	author = { BARTOLO R},
	title = {Closed geodesics in Finsler manifolds with boundary},
	year = {2013},
	booktitle = {International Meeting on Differential Geometry, Córdoba   2010},
	abstract = {We give a result about the existence of a closed geodesic on a Finsler manifold with boundary.},
	pages = {1--13}
}
@article{
	11589_7520,
	author = { Bartolo R  and  Candela A M  and  Salvatore A },
	title = {Infinitely many radial solutions of a non-homogeneous p-Laplacian problem},
	year = {2013},
	journal = {DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS},
	volume = {Supplement Volume},
	abstract = {In this paper we investigate the existence of infinitely many radial solutions for the elliptic Dirichlet problem
\[
\left\{
\begin{array}{ll}
\displaystyle{-\Delta_p u\ =|u|^{q-2}u + f} 
& \mbox{ in }  B_R,\\
 \displaystyle{u=\xi}  & \mbox{ on }  \partial B_R,\\
 \end{array}
\right.
\]
where $B_R$ is the open ball centered in $0$ with radius $R$ in $\R^N$ ($N\geq 3$), $2<p<q<p^\ast$, $\xi\in\R$ and $f$ is a continuous radial function in $\overline B_R$. The lack of even symmetry for the related functional is overcome by using some perturbative methods and the radial assumptions allow us to improve some previous results.},
	keywords = {p-Laplace operator; non-null boundary data; lack of symmetry},
	pages = {51--59}
}
@article{
	11589_1677,
	author = { Bartolo R  and  Candela A M  and  Salvatore A },
	title = {p-Laplacian problems with nonlinearities interacting with the spectrum},
	year = {2013},
	journal = {NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS},
	volume = {20},
	abstract = {The aim of this paper is investigating the existence and the multiplicity of solutions of the quasilinear elliptic problem
\[
\left\{
\begin{array}{ll}
\displaystyle{-\Delta_p u\ =\ g(x, u)} 
& \mbox{ in }  \Omega,\\
 \displaystyle{u=0}  & \mbox{ on }  \partial\Omega,\\
 \end{array}
\right.
\]
where $1<p<+\infty$, $\Delta_p u= {\rm div}(|\nabla u|^{p-2}\nabla u)$, $\Omega$ is an open bounded domain of $\R^N$ with smooth boundary $\partial\Omega$ and the nonlinearity $g$ behaves as $u^{p-1}$ at infinity. The main tools of the proof are some abstract critical point theorems in \cite{bbf}, but extended to Banach spaces, and two sequences of quasi--eigenvalues for the $p$--Laplacian operator as in \cite{cp, lz1}.},
	keywords = {Asymptotically p-linear problem; p-Laplacian; variational methods},
	doi = {10.1007/s00030-013-0226-1},	
	pages = {1701--1721}
}
@article{
	11589_1153,
	author = { BARTOLO R},
	title = {Infinitely many solutions for quasilinear elliptic problems with broken symmetry},
	year = {2013},
	journal = {ADVANCED NONLINEAR STUDIES},
	volume = {13},
	abstract = {{{\small The aim of this paper is investigating the existence of solutions of the quasilinear elliptic problem
$$
\leqno{(P_\varphi)}\qquad\qquad
\left\{
\begin{array}{ll}
\displaystyle{-\Delta_p u\ =|u|^{q-2}u + f} 
& \mbox{ in }  \Omega,\\
 \displaystyle{u=\varphi}  & \mbox{ on }  \partial\Omega,\\
 \end{array}
\right.
$$
where $\Omega$ is an open bounded domain of ${\bf R}^N$ with $C^2$ boundary $\partial\Omega$, $\Delta_p u= {\rm div}(|\nabla u|^{p-2}\nabla u)$, $1<p<q<p^\ast$, $f\in C(\overline\Omega)$ and $\varphi\in C^2(\overline\Omega)$. By means of the so-called Bolle's method in \cite{bolle, bgt}, we extend a result in \cite{gp} where the authors consider $\Omega = ]0,1[^N$ and $u=0$ on $\partial\Omega$.
}}
\end{center}},
	keywords = {p-Laplace operator; Non-homogeneous boundary data; Perturbative method},
	pages = {739--749}
}
@conference{
	11589_52712,
	author = { Bartolo R  and  Candela A M  and  Caponio E },
	title = {An Avez-Seifert type theorem for normal geodesics on a stationary spacetime},
	year = {2011},
	booktitle = {Advances in Lorentzian Geometry, AMS/IP Stud. Adv. Math. 49, Amer. Math. Soc., Providence, RI},
	pages = {1--9}
}
@article{
	11589_9794,
	author = { Bartolo R  and  Candela A M  and  Flores J L },
	title = {A note on geodesic connectedness of Gödel type spacetimes},
	year = {2011},
	journal = {DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS},
	volume = {29},
	abstract = {In this note we reduce the problem of geodesic connectedness in a wide class of Gödel type spacetimes to the search of critical points of a functional naturally involved in the study of geodesics in standard static spacetimes. Then, by using some known accurate results on the latter, we improve previous results on the former. (C) 2011 Elsevier B.V. All rights reserved.},
	keywords = {Geodesic connectedness, variational tools, Godel type spacetime, static spacetime, quadratic growth.},
	doi = {10.1016/j.difgeo.2011.08.006},	
	pages = {779--786}
}
@article{
	11589_52220,
	author = { Bartolo R  and  Caponio E  and  Germinario AV  and  Sanchez M },
	title = {Convex domains of Finsler and Riemannian manifolds},
	year = {2011},
	journal = {CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS},
	volume = {40},
	abstract = {"A detailed study of the notions of convexity for a hypersurface in a Finsler manifold is carried out. In particular, the infinitesimal and local notions of convexity are shown to be equivalent. Our approach differs from Bishop's one in his classical result (Bishop, Indiana Univ Math J 24:169-172, 1974) for the Riemannian case. Ours not only can be extended to the Finsler setting but it also reduces the typical requirements of differentiability for the metric and it yields consequences on the multiplicity of connecting geodesics in the convex domain defined by the hypersurface."},
	keywords = {Finsler metric, convex boundary, geodesic},
	doi = {10.1007/s00526-010-0343-1},	
	pages = {335--356}
}