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Eigenvalue results for pseudomonotone perturbations of maximal monotone operators

In-Sook Kim, Jung-Hyun Bae (2013)

Open Mathematics

Let X be an infinite-dimensional real reflexive Banach space such that X and its dual X* are locally uniformly convex. Suppose that T: X⊃D(T) → 2X* is a maximal monotone multi-valued operator and C: X⊃D(C) → X* is a generalized pseudomonotone quasibounded operator with L ⊂ D(C), where L is a dense subspace of X. Applying a recent degree theory of Kartsatos and Skrypnik, we establish the existence of an eigensolution to the nonlinear inclusion 0 ∈ T x + λ C x, with a regularization method by means...

Equation with residuated functions

Ray A. Cuninghame-Green, Karel Zimmermann (2001)

Commentationes Mathematicae Universitatis Carolinae

The structure of solution-sets for the equation F ( x ) = G ( y ) is discussed, where F , G are given residuated functions mapping between partially-ordered sets. An algorithm is proposed which produces a solution in the event of finite termination: this solution is maximal relative to initial trial values of x , y . Properties are defined which are sufficient for finite termination. The particular case of max-based linear algebra is discussed, with application to the synchronisation problem for discrete-event systems;...

Equilibrium of maximal monotone operator in a given set

Dariusz Zagrodny (2000)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Sufficient conditions for an equilibrium of maximal monotone operator to be in a given set are provided. This partially answers to a question posed in [10].

Evolution equations for a class of non­linear operators

Ennio De Giorgi, Marco Degiovanni, Antonio Marino, Mario Tosques (1983)

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

Se A è un operatore in uno spazio di Hilbert e V è un sotto insieme di questo spazio, in molti problemi si è indotti a modificare A sul «bordo» di V in modo da ottenere un operatore A tale che le soluzioni dell'equazione differenziale associata 0 ∈ U ′ + A ~ ⁢ ( U ) non escano da V . Se V non è convesso, l'operatore A non rientra nei casi classici esaminati, ad esempio, in [1]. In questo lavoro introduciamo alcune classi di operatori che contengono, in qualçhe caso significativo, quelli del genere sopra considerato...

Existence for implicit differential equations in Banach spaces

Viorel Barbu, Angelo Favini (1992)

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

We prove two existence results on abstract differential equations of the type d ⁢ B ⁢ u / d ⁢ t + A ⁢ u = f and we give some applications of them to partial differential equations.

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