1,721,032 research outputs found
Time periodic solutions for the nonlinear wave equation with long minimal period
No full textWe prove existence and multiplicity of small amplitude periodic solutions for the wave equation with small "mass" and odd nonlinearity. Such solutions bifurcate from resonant finite dimensional invariant tori of the fourth order Birkhoff normal form of the associated Hamiltonian system. The number of geometrically distinct solutions and their minimal periods go to infinity when the "mass" goes to zero. This is the first result about long minimal period for the autonomous wave equation. © 2006 Society for Industrial and Applied Mathematics
Periodic solutions of Birkhoff-Lewis type for the nonlinear wave equation
No full textWe prove the existence of infinitely many periodic solutions accumulating to zero for the one-dimensional nonlinear wave equation (vibrating string equation). The periods accumulate to zero and are both rational and irrational multiples of the string length
Periodic solutions of Birkhoff-Lewis type for the nonlinear wave equation
No full textWe prove existence and multiplicity of small amplitude periodic solutions with large period for the wave equation with small "mass". Such solutions bifurcate from resonant finite-dimensional invariant tori of the fourth order Birkhoff normal form of the associated hamiltonian system. The number of geometrically distinct solutions and their minimal periods tend to infinity when the "mass" tends to zero
A Birkhoff--Lewis type theorem for the nonlinear wave equation
No full textWe give an extension of the celebrated Birkhoff--Lewis theorem to
the nonlinear wave equation. Accordingly we find infinitely many
periodic orbits with longer and longer minimal periods
accumulating at the origin, which is an elliptic equilibrium of
the associated infinite dimensional Hamiltonian system.
Time periodic solutions for the nonlinear wave equation with long minimal period
No full textWe prove existence and multiplicity of small amplitude periodic
solutions for the wave equation with small ``mass'' and odd
nonlinearity. Such solutions bifurcate from resonant finite
dimensional invariant tori of the fourth order Birkhoff normal form of the
associated hamiltonian system. The number of geometrically
distinct solutions and their minimal periods go to infinity when
the ``mass'' goes to zero. This is the first result about long
minimal period for the autonomous wave equation
La cistectomia seminal-sparing nelle patologie non neoplastiche.
No full textPURPOSE. Seminal-sparing cystectomy is reported in literature only with reference to oncological conditions. However, it can be applied also in non-neoplastic conditions in young patients with good renal function. In the present report we will describe our experience in this field, with special reference to erectile function, urinary continence, fertility and feasibility. MATERIALS AND METHODS. Between 2000 and 2009 we have treated five patients with seminalsparing cystectomy for benign conditions, namely sclerosing cystitis, tuberculosis and a benign paraganglioma. All patients underwent a complete diagnostic evaluation including CT of upper abdomen and pelvis, and bone scintigraphy. Digital rectal examination was normal, PSA less than 2.5, with a free to total ratio above 25%. Cystectomy was performed, leaving in situ vas deferent, seminal vesicles, neurovascular bundles and prostatic capsule. Finally, an orthotopic bladder was performed. The ileal segment was anastomized to the prostatic capsule. RESULTS. All patients had uneventful recoveries and were continent within 2 weeks from the operation. Erectile function was maintained in all cases; in one patients fertility was preserved. CONCLUSIONS. In our experience, seminal–sparing cystectomy showed satisfactory clinical and functional preliminary results in selected patients. Young males, for whom maintenance of bladder function and sexual activity have a great impact on their quality of life, can be offered this alternative surgical procedure
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