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Banach spaces

Laurent Gruson, Marius van der Put (1974)

Mémoires de la Société Mathématique de France

Boundary value problem for an infinite system of second order differential equations in ℓ p spaces

Ishfaq Ahmad Malik, Tanweer Jalal (2020)

Mathematica Bohemica

The concept of measures of noncompactness is applied to prove the existence of a solution for a boundary value problem for an infinite system of second order differential equations in ℓ p space. We change the boundary value problem into an equivalent system of infinite integral equations and result is obtained by using Darbo’s type fixed point theorem. The result is illustrated with help of an example.

Boundary value problem for differential inclusions in Fréchet spaces with multiple solutions of the homogeneous problem

Irene Benedetti, Luisa Malaguti, Valentina Taddei (2011)

Mathematica Bohemica

The paper deals with the multivalued boundary value problem x ' ∈ A ( t , x ) x + F ( t , x ) for a.a. t ∈ [ a , b ] , M x ( a ) + N x ( b ) = 0 , in a separable, reflexive Banach space E . The nonlinearity F is weakly upper semicontinuous in x . We prove the existence of global solutions in the Sobolev space W 1 , p ( [ a , b ] , E ) with 1 < p < ∞ endowed with the weak topology. We consider the case of multiple solutions of the associated homogeneous linearized problem. An example completes the discussion.

Boundary value problems and periodic solutions for semilinear evolution inclusions

Nikolaos S. Papageorgiou (1994)

Commentationes Mathematicae Universitatis Carolinae

We consider boundary value problems for semilinear evolution inclusions. We establish the existence of extremal solutions. Using that result, we show that the evolution inclusion has periodic extremal trajectories. These results are then applied to closed loop control systems. Finally, an example of a semilinear parabolic distributed parameter control system is worked out in detail.

Bounded solutions on the Real line to non-autonomous Riccati Equations

Giuseppe Da Prato, Akira Ichikawa (1985)

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

Si dà un risultato di esistenza e unicità di una soluzione limitata in ] - ∞ , + ∞ [ per un'equazione di Riccati infinito-dimensionale.

BV solutions of rate independent differential inclusions

Pavel Krejčí, Vincenzo Recupero (2014)

Mathematica Bohemica

We consider a class of evolution differential inclusions defining the so-called stop operator arising in elastoplasticity, ferromagnetism, and phase transitions. These differential inclusions depend on a constraint which is represented by a convex set that is called the characteristic set. For BV (bounded variation) data we compare different notions of BV solutions and study how the continuity properties of the solution operators are related to the characteristic set. In the finite-dimensional case...

Carathéodory solutions of Sturm-Liouville dynamic equation with a measure of noncompactness in Banach spaces

Ahmet Yantir, Ireneusz Kubiaczyk, Aneta Sikorska-Nowak (2015)

Open Mathematics

In this paper, we present the existence result for Carathéodory type solutions for the nonlinear Sturm- Liouville boundary value problem (SLBVP) in Banach spaces on an arbitrary time scale. For this purpose, we introduce an equivalent integral operator to the SLBVP by means of Green’s function on an appropriate set. By imposing the regularity conditions expressed in terms of Kuratowski measure of noncompactness, we prove the existence of the fixed points of the equivalent integral operator. Mönch’s...

Classical solutions of parabolic equations in Hölder spaces

Eugenio Sinestrari (1983)

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

Sono dati nuovi teoremi di esistenza per soluzioni regolari di equazioni di evoluzione paraboliche astratte con applicazioni all'equazione del calore in spazi di funzioni holderiane e alle equazioni semilineari.

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