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Biduals of tensor products in operator spaces

Verónica Dimant, Maite Fernández-Unzueta (2015)

Studia Mathematica

We study whether the operator space V * * α W * * can be identified with a subspace of the bidual space ( V α W ) * * , for a given operator space tensor norm. We prove that this can be done if α is finitely generated and V and W are locally reflexive. If in addition the dual spaces are locally reflexive and the bidual spaces have the completely bounded approximation property, then the identification is through a complete isomorphism. When α is the projective, Haagerup or injective norm, the hypotheses can be weakened.

Bifurcation of free vibrations for completely resonant wave equations

Massimiliano Berti, Philippe Bolle (2004)

Bollettino dell'Unione Matematica Italiana

We prove existence of small amplitude, 2p/v-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions for any frequency ω belonging to a Cantor-like set of positive measure and for a generic set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem.

Bifurcation of periodic solutions to nonlinear measure differential equations

Maria Carolina Mesquita, Milan Tvrdý (2025)

Czechoslovak Mathematical Journal

The paper is devoted to the periodic bifurcation problems for generalizations of ordinary differential systems. The bifurcation is understood in the static sense of Krasnoselski and Zabreko. First, the conditions necessary for the given point to be bifurcation point for non autonomous generalized ordinary differential equations (based on the Kurzweil gauge type generalized integral) are proved. Then, as the main contribution, analogous results are obtained also for the nonlinear non autonomous measure...

Bifurcation theorems for nonlinear problems with lack of compactness

Francesca Faraci, Roberto Livrea (2003)

Annales Polonici Mathematici

We deal with a bifurcation result for the Dirichlet problem ⎧ - Δ p u = μ / | x | p | u | p - 2 u + λ f ( x , u ) a.e. in Ω, ⎨ ⎩ u | Ω = 0 . Starting from a weak lower semicontinuity result by E. Montefusco, which allows us to apply a general variational principle by B. Ricceri, we prove that, for μ close to zero, there exists a positive number λ * μ such that for every λ ] 0 , λ * μ [ the above problem admits a nonzero weak solution u λ in W 1 , p ( Ω ) satisfying l i m λ 0 | | u λ | | = 0 .

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