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Abstract semilinear equations in Banach spaces

Eugenio Sinestrari (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si studiano le proprietà delle soluzioni dell'equazione semilineare astratta u ( t ) = Λ u ( t ) + φ ( t , u ( t ) ) quando Λ è il generatore infinitesimale di un semigruppo analitico in uno spazio di Banach. Vengono provati nuovi teoremi di regolarità anche nel caso in cui φ non è continuo in tutto lo spazio.

Adjoint bi-continuous semigroups and semigroups on the space of measures

Bálint Farkas (2011)

Czechoslovak Mathematical Journal

For a given bi-continuous semigroup ( T ( t ) ) t 0 on a Banach space X we define its adjoint on an appropriate closed subspace X of the norm dual X ' . Under some abstract conditions this adjoint semigroup is again bi-continuous with respect to the weak topology σ ( X , X ) . We give the following application: For Ω a Polish space we consider operator semigroups on the space C b ( Ω ) of bounded, continuous functions (endowed with the compact-open topology) and on the space M ( Ω ) of bounded Baire measures (endowed with the weak * -topology)....

An irreducible semigroup of idempotents

Roman Drnovšek (1997)

Studia Mathematica

We construct a semigroup of bounded idempotents with no nontrivial invariant closed subspace. This answers a question which was open for some time.

An iterative algorithm by viscosity approximation method for mixed equilibrium problems, variational inclusion and fixed point of an infinite family of pseudo-contractive mappings

Phayap Katchang, Poom Kumam (2011)

Banach Center Publications

The purpose of this paper is to investigate the problem of finding a common element of the set of solutions for mixed equilibrium problems, the set of solutions of the variational inclusion problems for inverse strongly monotone mappings and the set of common fixed points for an infinite family of strictly pseudo-contractive mappings in the setting of Hilbert spaces. We prove the strong convergence theorem by using the viscosity approximation method for finding the common element of the above four...

Analytic semigroups generated on a functional extrapolation space by variational elliptic equations

Vincenzo Vespri (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We prove that any elliptic operator of second order in variational form is the infinitesimal generator of an analytic semigroup in the functional space C - 1 , α ( Ω ) consinsting of all derivatives of hölder-continuous functions in Ω where Ω is a domain in n not necessarily bounded. We characterize, moreover the domain of the operator and the interpolation spaces between this and the space C - 1 , α ( Ω ) . We prove also that the spaces C - 1 , α ( Ω ) can be considered as extrapolation spaces relative to suitable non-variational operators....

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