On the existence of viable solutions for a class of second order differential inclusions

Aurelian Cernea

Displaying similar documents to “On the existence of viable solutions for a class of second order differential inclusions”

Monotone extenders for bounded c-valued functions

Kaori Yamazaki (2010)

Studia Mathematica

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Let c be the Banach space consisting of all convergent sequences of reals with the sup-norm, $C_{\infty} (A, c)$ the set of all bounded continuous functions f: A → c, and $C_{A} (X, c)$ the set of all functions f: X → c which are continuous at each point of A ⊂ X. We show that a Tikhonov subspace A of a topological space X is strong Choquet in X if there exists a monotone extender $u : C_{\infty} (A, c) \to C_{A} (X, c)$ . This shows that the monotone extension property for bounded c-valued functions can fail in GO-spaces, which provides a negative answer...

On the Rockafellar theorem for $Φ^{γ (\cdot, \cdot)}$ -monotone multifunctions

S. Rolewicz (2006)

Studia Mathematica

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Let X be an arbitrary set, and γ: X × X → ℝ any function. Let Φ be a family of real-valued functions defined on X. Let $Γ : X \to 2^{Φ}$ be a cyclic $Φ^{γ (\cdot, \cdot)}$ -monotone multifunction with non-empty values. It is shown that the following generalization of the Rockafellar theorem holds. There is a function f: X → ℝ such that Γ is contained in the $Φ^{γ (\cdot, \cdot)}$ -subdifferential of f, $Γ (x) \subset \partial_{Φ}^{γ (\cdot, \cdot)} {f |}_{x}$ .

On a proof of the boundedness and nuclearity of pseudodifferential operators in $R^{n}$

Jan A. Rempała (1990)

Annales Polonici Mathematici

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Can we assign the Borel hulls in a monotone way?

Márton Elekes, András Máthé (2009)

Fundamenta Mathematicae

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A hull of A ⊆ [0,1] is a set H containing A such that λ*(H) = λ*(A). We investigate all four versions of the following problem. Does there exist a monotone (with respect to inclusion) map that assigns a Borel/ $G_{δ}$ hull to every negligible/measurable subset of [0,1]? Three versions turn out to be independent of ZFC, while in the fourth case we only prove that the nonexistence of a monotone $G_{δ}$ hull operation for all measurable sets is consistent. It remains open whether existence here is also...

Isomorphic properties in spaces of compact operators

Ioana Ghenciu (2023)

Commentationes Mathematicae Universitatis Carolinae

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We introduce the definition of $p$ -limited completely continuous operators, $1 \leq p < \infty$ . The question of whether a space of operators has the property that every $p$ -limited subset is relative compact when the dual of the domain and the codomain have this property is studied using $p$ -limited completely continuous evaluation operators.

Nonlinear multivalued boundary value problems

Ralf Bader, Nikolaos S. Papageorgiou (2001)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper, we study nonlinear second order differential inclusions with a multivalued maximal monotone term and nonlinear boundary conditions. We prove existence theorems for both the convex and nonconvex problems, when $d o m A \neq ℝ^{N}$ and $d o m A = ℝ^{N}$ , with A being the maximal monotone term. Our formulation incorporates as special cases the Dirichlet, Neumann and periodic problems. Our tools come from multivalued analysis and the theory of nonlinear monotone operators.

The Embeddability of c₀ in Spaces of Operators

Ioana Ghenciu, Paul Lewis (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

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Results of Emmanuele and Drewnowski are used to study the containment of c₀ in the space $K_{w *} (X *, Y)$ , as well as the complementation of the space $K_{w *} (X *, Y)$ of w*-w compact operators in the space $L_{w *} (X *, Y)$ of w*-w operators from X* to Y.

A note on locally convex spaces with a basic sequence of $β$ -disks

B. Mirković (1970)

Matematički Vesnik

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Multiple summing operators on $l_{p}$ spaces

Dumitru Popa (2014)

Studia Mathematica

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We use the Maurey-Rosenthal factorization theorem to obtain a new characterization of multiple 2-summing operators on a product of $l_{p}$ spaces. This characterization is used to show that multiple s-summing operators on a product of $l_{p}$ spaces with values in a Hilbert space are characterized by the boundedness of a natural multilinear functional (1 ≤ s ≤ 2). We use these results to show that there exist many natural multiple s-summing operators $T : l_{4 / 3} \times l_{4 / 3} \to l ₂$ such that none of the associated linear operators...

On hyponormal operators in Krein spaces

Kevin Esmeral, Osmin Ferrer, Jorge Jalk, Boris Lora Castro (2019)

Archivum Mathematicum

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In this paper the hyponormal operators on Krein spaces are introduced. We state conditions for the hyponormality of bounded operators focusing, in particular, on those operators $T$ for which there exists a fundamental decomposition $𝕂 = 𝕂^{+} \oplus 𝕂^{-}$ of the Krein space $𝕂$ with $𝕂^{+}$ and $𝕂^{-}$ invariant under $T$ .

$H^{\infty}$ functional calculus for sectorial and bisectorial operators

Giovanni Dore, Alberto Venni (2005)

Studia Mathematica

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We give a concise exposition of the basic theory of $H^{\infty}$ functional calculus for N-tuples of sectorial or bisectorial operators, with respect to operator-valued functions; moreover we restate and prove in our setting a result of N. Kalton and L. Weis about the boundedness of the operator $f (T ₁, . . ., T_{N})$ when f is an R-bounded operator-valued holomorphic function.

Monotone substochastic operators and a new Calderón couple

Karol Leśnik (2015)

Studia Mathematica

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An important result on submajorization, which goes back to Hardy, Littlewood and Pólya, states that b ⪯ a if and only if there is a doubly stochastic matrix A such that b = Aa. We prove that under monotonicity assumptions on the vectors a and b the matrix A may be chosen monotone. This result is then applied to show that $(\tilde{L^{p}}, L^{\infty})$ is a Calderón couple for 1 ≤ p < ∞, where $\tilde{L^{p}}$ is the Köthe dual of the Cesàro space $C e s_{p^{'}}$ (or equivalently the down space $L_{↓}^{p^{'}}$ ). In particular, $(\tilde{L ¹}, L^{\infty})$ is a Calderón couple, which...

The natural linear operators $T * ⇝ T T^{(r)}$

J. Kurek, W. M. Mikulski (2003)

Colloquium Mathematicae

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For natural numbers n ≥ 3 and r a complete description of all natural bilinear operators $T * \times_{ℳ f ₙ} T^{(0, 0)} ⇝ T^{(0, 0)} T^{(r)}$ is presented. Next for natural numbers r and n ≥ 3 a full classification of all natural linear operators $T *_{| ℳ f ₙ} ⇝ T T^{(r)}$ is obtained.

Absolutely continuous linear operators on Köthe-Bochner spaces

(2011)

Banach Center Publications

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Let E be a Banach function space over a finite and atomless measure space (Ω,Σ,μ) and let $(X, | | \cdot | |_{X})$ and $(Y, | | \cdot | |_{Y})$ be real Banach spaces. A linear operator T acting from the Köthe-Bochner space E(X) to Y is said to be absolutely continuous if $| | T (1_{A ₙ} f) {| |}_{Y} \to 0$ whenever μ(Aₙ) → 0, (Aₙ) ⊂ Σ. In this paper we examine absolutely continuous operators from E(X) to Y. Moreover, we establish relationships between different classes of linear operators from E(X) to Y.

Minimax theorems without changeless proportion

Liang-Ju Chu, Chi-Nan Tsai (2003)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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The so-called minimax theorem means that if X and Y are two sets, and f and g are two real-valued functions defined on X×Y, then under some conditions the following inequality holds: $i n f_{y \in Y} s u p_{x \in X} f (x, y) \leq s u p_{x \in X} i n f_{y \in Y} g (x, y)$ . We will extend the two functions version of minimax theorems without the usual condition: f ≤ g. We replace it by a milder condition: $s u p_{x \in X} f (x, y) \leq s u p_{x \in X} g (x, y)$ , ∀y ∈ Y. However, we require some restrictions; such as, the functions f and g are jointly upward, and their upper sets are connected. On the other hand, by using some...

A fixed point theorem for mappings with a $Ψ$ -densifying iteration in locally convex spaces

O. Hadžić (1978)

Matematički Vesnik

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A penalty approach for a box constrained variational inequality problem

Zahira Kebaili, Djamel Benterki (2018)

Applications of Mathematics

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We propose a penalty approach for a box constrained variational inequality problem $(BVIP)$ . This problem is replaced by a sequence of nonlinear equations containing a penalty term. We show that if the penalty parameter tends to infinity, the solution of this sequence converges to that of $BVIP$ when the function $F$ involved is continuous and strongly monotone and the box $C$ contains the origin. We develop the algorithmic aspect with theoretical arguments properly established. The numerical results...

On the Existence of Solutions for Abstract Nonlinear Operator Equations

Marek Galewski (2007)

Bollettino dell'Unione Matematica Italiana

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We provide a duality theory and existence results for a operator equation $\nabla T(x)=\nabla N(x)$ where $T$ is not necessarily a monotone operator. We use the abstract version of the so called dual variational method. The solution is obtained as a limit of a minimizng sequence whose existence and convergence is proved.

Operator $e^{- λ s^{α}}$

A. Takači (1978)

Matematički Vesnik

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Spaces of compact operators on $C (2^{} \times [0, α])$ spaces

Elói Medina Galego (2011)

Colloquium Mathematicae

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We classify, up to isomorphism, the spaces of compact operators (E,F), where E and F are the Banach spaces of all continuous functions defined on the compact spaces $2^{} \times [0, α]$ , the topological products of Cantor cubes $2^{}$ and intervals of ordinal numbers [0,α].

Stability of infinite ranges and kernels

K.-H. Förster, V. Müller (2006)

Studia Mathematica

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Let A(·) be a regular function defined on a connected metric space G whose values are mutually commuting essentially Kato operators in a Banach space. Then the spaces $R^{\infty} (A (z))$ and $\bar{N^{\infty} (A (z))}$ do not depend on z ∈ G. This generalizes results of B. Aupetit and J. Zemánek.

A note on the commutator of two operators on a locally convex space

Edvard Kramar (2016)

Commentationes Mathematicae Universitatis Carolinae

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Denote by $C$ the commutator $A B - B A$ of two bounded operators $A$ and $B$ acting on a locally convex topological vector space. If $A C - C A = 0$ , we show that $C$ is a quasinilpotent operator and we prove that if $A C - C A$ is a compact operator, then $C$ is a Riesz operator.

$α$ -continuous multivalued maps

J. Eweret (1989)

Matematički Vesnik

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