Scientific Reports
The preprint collection of the Department of Mathematics.
Full-text generally not available for preprints prior to may 2006.
Found 866 products
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QDD185 - 07/08/2014
Barutello,V.; Boscaggin, A.; Verzini, G.
Positive solutions with a complex behavior for superlinear indefinite ODEs on the real line | Abstract | | We show the existence of infinitely many positive solutions, defined on the real line,for the nonlinear scalar ODE ....,where a is a periodic,
sign-changing function, and the parameter ? > 0 is large. Such solutions are characterized by the fact of being either small or large in each interval of positivity of a. In this way, we find periodic solutions, having minimal period arbitrarily large, and bounded non-periodic solutions, exhibiting a complex behavior. The proof is variational, exploiting suitable natural constraints of Nehari type.
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QDD183 - 06/10/2014
Gazzola, F.; Karageorgis, P.
Refined blow-up results for nonlinear fourth order differential equations | Abstract | | We study a class of nonlinear fourth order differential equations which arise as models of suspension bridges. When it comes to power-like nonlinearities, it is known that solutions may blow up in finite time, if the initial data satisfy some positivity assumption. We extend this result to more general nonlinearities allowing exponential growth and to a wider class of initial data. We also give some hints on how to prevent blow-up. |
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QDD184 - 06/10/2014
Cao, H.D.; Catino, G.; Chen, Q.; Mantegazza, C.; Mazzieri, L.
Bach-flat gradient steady Ricci solitons | Abstract | | Abstract. In this paper we prove that any n-dimensional (n ? 4) complete Bach-flat gradient steady Ricci soliton with positive Ricci curvature is isometric to the Bryant soliton. We also show that a three-dimensional gradient steady Ricci soliton with divergence-free Bach tensor is either flat or isometric to the Bryant soliton. In particular, these results improve the corresponding classification theorems for complete locally conformally flat gradient steady Ricci solitons in [8, 10].
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QDD182 - 05/22/2014
Noris, B.; Tavares, H.; Verzini, G.
Stable solitary waves with prescribed L2 mass for the cubic Schrodinger system with trapping potentials | Abstract | | For the cubic Schrodinger system with trapping potentials in RN, N <= 3, or in bounded domains, we investigate the existence and the orbital stability of standing waves having components with prescribed L2 mass provide a variational characterization of such solutions, which gives information on the stability through of a condition of Grillakis-Shatah-Strauss type. As an application, we show existence of conditionally orbitally stable solitary waves when: a) the masses are small, for almost every scattering lengths, and b) in the defocusing, weakly interacting case, for any masses. |
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QDD181 - 05/12/2014
Gazzola, F.; Jleli, M.; Samet, B.
On the Melan equation for suspension bridges | Abstract | | We ?rst recall how the classical Melan equation for suspension bridges is derived. We discuss the origin of its nonlinearity and the possible form of the nonlocal term: we show that some alternative forms may lead to fairly different responses. Then we prove several existence results through ?xed points theorems applied to suitable maps. The problem appears to be ill posed: we exhibit a counterexample to uniqueness. Finally, we implement a numerical procedure in order to try to approximate the solution; it turns out that the ?xed point may be quite unstable for actual suspension bridges. Several open problems are suggested. |
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QDD180 - 05/08/2014
Gregoratti, M.
The Hamiltonian generating Quantum Stochastic Evolutions in the limit from Repeated to Continuous Interactions | Abstract | | We consider a quantum stochastic evolution in continuous time defined by the quantum stochastic differential equation of Hudson and Parthasarathy. On one side, such an evolution can be defined also by a standard Schroedinger equation with a singular and unbounded Hamiltonian operator K. On the other side, such an evolution can be obtained also as a limit from Hamiltonian repeated interactions in discrete time. We study how the structure of the Hamiltonian K emerges in the limit from repeated to continuous interactions. We present results in the case of 1-dimensional multiplicity and system spaces, where calculations can be explicitly performed, and the proper formulation of the problem can be discussed. |
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QDD179 - 05/06/2014
Guatteri, G.; Tessitore, G.
Well Posedness of Operator Valued Backward Stochastic Riccati Equations in Infinite Dimensional Spaces | Abstract | | We prove existence and uniqueness of the mild solution of an infi nite dimensional,
operator valued, backward stochastic Riccati equation. We exploit the regularizing properties of the semigroup generated by the unbounded operator involved in the equation. Then the results will be applied to characterize the value function and optimal feedback law for a infi nite dimensional, linear quadratic control problem with stochastic coefficients.
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QDD178 - 05/05/2014
G. Fusai, G. Germano, D. Marazzina
Fast pricing of discretely monitored exotic options based on the Spitzer identity and the Wiener-Hopf factorization | Abstract | | We present a fast and accurate pricing technique based on the Spitzer identity and the Wiener-Hopf factorization. We apply it to barrier and lookback options when the monitoring is discrete and the underlying evolves according to an exponential L'evy process. The numerical implementation exploits the fast Fourier transform and the Euler summation. The computational cost is independent of the number of monitoring dates; the error decays exponentially with the number of grid points, except for double-barrier options. |
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