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Rossella Bartolo
Ruolo
Ricercatore
Organizzazione
Politecnico di Bari
Dipartimento
Dipartimento di Meccanica, Matematica e Management
Area Scientifica
Area 01 - Scienze matematiche e informatiche
Settore Scientifico Disciplinare
MAT/05 - Analisi Matematica
Settore ERC 1° livello
PE - Physical sciences and engineering
Settore ERC 2° livello
PE1 Mathematics: All areas of mathematics, pure and applied, plus mathematical foundations of computer science, mathematical physics and statistics
Settore ERC 3° livello
PE1_8 Analysis
We give a result about the existence of a closed geodesic on a Finsler manifold with boundary.
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.
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.
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} ight. ] where $B_R$ is the open ball centered in $0$ with radius $R$ in $R^N$ ($Ngeq 3$), $2<p<q<p^ast$, $xiinR$ 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.
By using variational methods we prove the multiplicity of weak solutions of a class of asymptotically p-linear problems.
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 } partialOmega,\ end{array} ight. end{equation} where $Omega$ is an open bounded domain of $R^N$, $varepsiloninR$, $p$ 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.
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 } partialOmega,\ end{array} ight. ] where $1<p<+infty$, $Delta_p u= { m div}(|nabla u|^{p-2}nabla u)$, $Omega$ is an open bounded domain of $R^N$ with smooth boundary $partialOmega$ 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}.
{{small The aim of this paper is investigating the existence of solutions of the quasilinear elliptic problem $$ leqno{(P_varphi)}qquadqquad left{ begin{array}{ll} displaystyle{-Delta_p u =|u|^{q-2}u + f} & mbox{ in } Omega,\ displaystyle{u=varphi} & mbox{ on } partialOmega,\ end{array} ight. $$ where $Omega$ is an open bounded domain of ${bf R}^N$ with $C^2$ boundary $partialOmega$, $Delta_p u= { m div}(|nabla u|^{p-2}nabla u)$, $1<p<q<p^ast$, $fin C(overlineOmega)$ and $varphiin C^2(overlineOmega)$. 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 $partialOmega$. }} end{center}
"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."
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