TY - JOUR
T1 - Forced Vibrations of a Nonhomogeneous String
JF - SIAM J. Math. Anal. 40 (2008) 382-412
Y1 - 2008
A1 - P Baldi
A1 - Massimiliano Berti
AB - We prove existence of vibrations of a nonhomogeneous string under a nonlinear time periodic forcing term in the case in which the forcing frequency avoids resonances with the vibration modes of the string (nonresonant case). The proof relies on a Lyapunov-Schmidt reduction and a Nash-Moser iteration scheme.
UR - http://hdl.handle.net/1963/2643
U1 - 1480
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Forced vibrations of wave equations with non-monotone nonlinearities
JF - Ann. Inst. H. PoincarĂ© Anal. Non LinĂ©aire 23 (2006) 439-474
Y1 - 2006
A1 - Massimiliano Berti
A1 - Luca Biasco
AB - We prove existence and regularity of periodic in time solutions of completely resonant nonlinear forced wave equations with Dirichlet boundary conditions for a large class of non-monotone forcing terms. Our approach is based on a variational Lyapunov-Schmidt reduction. It turns out that the infinite dimensional bifurcation equation exhibits an intrinsic lack of compactness. We solve it via a minimization argument and a-priori estimate methods inspired to regularity theory of Rabinowitz.
UR - http://hdl.handle.net/1963/2160
U1 - 2084
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Fast Arnold diffusion in systems with three time scales
JF - Discrete Contin. Dyn. Syst. 8 (2002) 795-811
Y1 - 2002
A1 - Massimiliano Berti
A1 - Philippe Bolle
AB - We consider the problem of Arnold Diffusion for nearly integrable partially isochronous Hamiltonian systems with three time scales. By means of a careful shadowing analysis, based on a variational technique, we prove that, along special directions, Arnold diffusion takes place with fast (polynomial) speed, even though the \\\"splitting determinant\\\" is exponentially small.
PB - American Institute of Mathematical Sciences
UR - http://hdl.handle.net/1963/3058
U1 - 1275
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - A functional analysis approach to Arnold diffusion
JF - Ann. Inst. H. Poincare Anal. Non Lineaire 19 (2002) 395-450
Y1 - 2002
A1 - Massimiliano Berti
A1 - Philippe Bolle
AB - We discuss in the context of nearly integrable Hamiltonian systems a functional analysis approach to the \\\"splitting of separatrices\\\" and to the \\\"shadowing problem\\\". As an application we apply our method to the problem of Arnold Diffusion for nearly integrable partially isochronous systems improving known results.
PB - Elsevier
UR - http://hdl.handle.net/1963/3151
U1 - 1182
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -