An existence theorem for non-homogeneous differential inclusions in Sobolev spaces

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Jean-Philippe Mandallena ◽  
Mikhail Sychev
Keyword(s):  
Existence Theorem ◽  
Sobolev Spaces ◽  
Differential Inclusions ◽  
Existence Theorems ◽  
Lipschitz Functions ◽  
Higher Regularity ◽  
Funct Anal

Abstract In the present paper, we establish an existence theorem for non-homogeneous differential inclusions in Sobolev spaces. This theorem extends the results of Müller and Sychev [S. Müller and M. A. Sychev, Optimal existence theorems for nonhomogeneous differential inclusions, J. Funct. Anal. 181 2001, 2, 447–475; M. A. Sychev, Comparing various methods of resolving differential inclusions, J. Convex Anal. 18 2011, 4, 1025–1045] obtained in the setting of Lipschitz functions. We also show that solutions can be selected with the property of higher regularity.

scholarly journals Some existence theorems for differential inclusions in Hilbert spaces

1996 ◽  
Vol 54 (2) ◽  
pp. 317-327 ◽  
Author(s):  
Shih-Sen Chang ◽  
Yu-Qing Chen ◽  
Byung Soo Lee
Keyword(s):  
Existence Theorem ◽  
Hilbert Spaces ◽  
Differential Inclusions ◽  
Existence Theorems ◽  
Monotone Type

Some existence theorem for solutions of two kinds of differential inclusions with monotone type mappings in Hilbert spaces are given.

scholarly journals Existence Theorems ofε-Cone Saddle Points for Vector-Valued Mappings

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Tao Chen
Keyword(s):  
Saddle Point ◽  
Existence Theorem ◽  
Equilibrium Problem ◽  
Existence Result ◽  
Existence Theorems ◽  
Saddle Points ◽  
Vector Equilibrium Problem ◽  
Saddle Point Theorem ◽  
Vector Equilibrium ◽  
Vector Valued

A new existence result ofε-vector equilibrium problem is first obtained. Then, by using the existence theorem ofε-vector equilibrium problem, a weaklyε-cone saddle point theorem is also obtained for vector-valued mappings.

scholarly journals Equilibrium points of random generalized games

1998 ◽  
Vol 21 (4) ◽  
pp. 791-800 ◽  
Author(s):  
E. Tarafdar ◽  
Xian-Zhi Yuan
Keyword(s):  
Existence Theorem ◽  
Existence Theorems ◽  
Equilibrium Points ◽  
Lower Semicontinuous ◽  
Vector Spaces ◽  
Maximal Elements ◽  
Equilibrium Existence ◽  
Topological Vector Spaces ◽  
Generalized Games ◽  
Random Games

In this paper, the concepts of random maximal elements, random equilibria and random generalized games are described. Secondly by measurable selection theorem, some existence theorems of random maximal elements forLc-majorized correspondences are obtained. Then we prove existence theorems of random equilibria for non-compact one-person random games. Finally, a random equilibrium existence theorem for non-compact random generalized games (resp., random abstract economics) in topological vector spaces and a random equilibrium existence theorem of non-compact random games in locally convex topological vector spaces in which the constraint mappings are lower semicontinuous with countable number of players (resp., agents) are given. Our results are stochastic versions of corresponding results in the recent literatures.

scholarly journals Maximal elements and equilibria of generalized games for𝒰-majorized and condensing correspondences

1999 ◽  
Vol 22 (1) ◽  
pp. 179-189 ◽  
Author(s):  
George Xian-Zhi Yuan ◽  
E. Tarafdar
Keyword(s):  
Existence Theorem ◽  
Existence Theorems ◽  
Vector Spaces ◽  
Maximal Elements ◽  
Topological Vector Spaces ◽  
New Type ◽  
Generalized Games ◽  
Locally Convex ◽  
Qualitative Games

In this paper, we first give an existence theorem of maximal elements for a new type of preference correspondences which are𝒰-majorized. Then some existence theorems for compact (resp., non-compact) qualitative games and generalized games in which the constraint or preference correspondences are𝒰-majorized (resp.,Ψ-condensing) are obtained in locally convex topological vector spaces.

scholarly journals Corrigendum to “Hardy Sobolev spaces on strongly Lipschitz domains of Rn” [J. Funct. Anal. 218 (2005) 54–109]

2007 ◽  
Vol 253 (2) ◽  
pp. 782-785
Author(s):  
Pascal Auscher ◽  
Emmanuel Russ ◽  
Philippe Tchamitchian
Keyword(s):  
Sobolev Spaces ◽  
Lipschitz Domains ◽  
Funct Anal

scholarly journals Existence Results for Generalized Bagley-Torvik Type Fractional Differential Inclusions with Nonlocal Initial Conditions

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Lizhen Chen ◽  
Gang Li
Keyword(s):  
Differential Inclusions ◽  
Initial Conditions ◽  
Existence Theorems ◽  
Nonlocal Conditions ◽  
Existence Results ◽  
Lipschitz Continuous ◽  
Nonlocal Initial Conditions ◽  
Nonlinear Alternative ◽  
Noncompactness Measure ◽  
Fractional Differential

In this article, we prove the existence of solutions for the generalized Bagley-Torvik type fractional order differential inclusions with nonlocal conditions. It allows applying the noncompactness measure of Hausdorff, fractional calculus theory, and the nonlinear alternative for Kakutani maps fixed point theorem to obtain the existence results under the assumptions that the nonlocal item is compact continuous and Lipschitz continuous and multifunction is compact and Lipschitz, respectively. Our results extend the existence theorems for the classical Bagley-Torvik inclusion and some related models.

Model existence theorems for modal and intuitionistic logics

1973 ◽  
Vol 38 (4) ◽  
pp. 613-627 ◽  
Author(s):  
Melvin Fitting
Keyword(s):  
Existence Theorem ◽  
Intuitionistic Logic ◽  
Classical Logic ◽  
Existence Theorems ◽  
Compactness Theorem ◽  
Infinitary Logic ◽  
Consistency Property ◽  
Model Existence ◽  
Model Existence Theorem ◽  
Intuitionistic Logics

In classical logic a collection of sets of statements (or equivalently, a property of sets of statements) is called a consistency property if it meets certain simple closure conditions (a definition is given in §2). The simplest example of a consistency property is the collection of all consistent sets in some formal system for classical logic. The Model Existence Theorem then says that any member of a consistency property is satisfiable in a countable domain. From this theorem many basic results of classical logic follow rather simply: completeness theorems, the compactness theorem, the Lowenheim-Skolem theorem, and the Craig interpolation lemma among others. The central position of the theorem in classical logic is obvious. For the infinitary logic the Model Existence Theorem is even more basic as the compactness theorem is not available; [8] is largely based on it.In this paper we define appropriate notions of consistency properties for the first-order modal logics S4, T and K (without the Barcan formula) and for intuitionistic logic. Indeed we define two versions for intuitionistic logic, one deriving from the work of Gentzen, one from Beth; both have their uses. Model Existence Theorems are proved, from which the usual known basic results follow. We remark that Craig interpolation lemmas have been proved model theoretically for these logics by Gabbay ([5], [6]) using ultraproducts. The existence of both ultra-product and consistency property proofs of the same result is a common phenomena in classical and infinitary logic. We also present extremely simple tableau proof systems for S4, T, K and intuitionistic logics, systems whose completeness is an easy consequence of the Model Existence Theorems.

scholarly journals An Existence Theorem for Fractional Hybrid Differential Inclusions of Hadamard Type with Dirichlet Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Existence Theorem ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Dirichlet Boundary ◽  
Existence Of Solutions ◽  
Dirichlet Boundary Conditions

This paper studies the existence of solutions for a boundary value problem of nonlinear fractional hybrid differential inclusions by using a fixed point theorem due to Dhage (2006). The main result is illustrated with the aid of an example.

Existence Theorems for Periodic Differential Inclusions in ℝ N

2004 ◽  
Vol 20 (2) ◽  
pp. 179-190
Author(s):  
Michael Filippakis ◽  
Leszek Gasinski ◽  
Nikolaos S. Papageorgiou
Keyword(s):  
Differential Inclusions ◽  
Existence Theorems
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