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.

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 Noncompact Perturbation of Sweeping Process with Delay in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
F. Aladsani ◽  
A. G. Ibrahim
Keyword(s):  
Existence Theorem ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Convex Sets ◽  
Existence Of Solutions ◽  
Existence Theorems ◽  
Existence Results ◽  
Sweeping Process ◽  
Evolution Inclusion ◽  
Sweeping Processes

We have proven an existence theorem concerning the existence of solutions for a functional evolution inclusion governed by sweeping process with closed convex sets depending on time and state and with a noncompact nonconvex perturbation in Banach spaces. This work extends some recent existence theorems concerning sweeping processes from Hilbert spaces setting to Banach spaces setting. Moreover, it improves some recent existence results for sweeping processes in Banach spaces.

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 NONLINEAR DIFFERENTIAL INCLUSIONS OF SEMIMONOTONE AND CONDENSING TYPE IN HILBERT SPACES

2015 ◽  
Vol 52 (2) ◽  
pp. 421-438
Author(s):  
Hossein Abedi ◽  
Ruhollah Jahanipur
Keyword(s):  
Hilbert Spaces ◽  
Differential Inclusions ◽  
Nonlinear Differential Inclusions

On some differential inclusions in Hilbert spaces

1997 ◽  
Vol 29 (1) ◽  
pp. 65-76
Author(s):  
Bui An Ton
Keyword(s):  
Hilbert Spaces ◽  
Differential Inclusions

Existence Theorems for Some Weak Abstract Variable Domain Hyperbolic Problems

1971 ◽  
Vol 23 (4) ◽  
pp. 611-626 ◽  
Author(s):  
Robert Carroll ◽  
Emile State
Keyword(s):  
Hilbert Spaces ◽  
Differential Operators ◽  
Separable Hilbert Space ◽  
Hyperbolic Equations ◽  
Existence Theorems ◽  
Hyperbolic Problems ◽  
Linear Maps ◽  
Variable Domains ◽  
Elliptic Differential Operators ◽  
Image Position

In this paper we prove some existence theorems for some weak problems with variable domains arising from hyperbolic equations of the type1.1where A = {A(t)} is, for example, a family of elliptic differential operators in space variables x = (x1, …, xn). Thus let H be a separable Hilbert space and let V(t) ⊂ H be a family of Hilbert spaces dense in H with continuous injections i(t): V(t) → H (0 ≦ t ≦ T < ∞). Let V’ (t) be the antidual of V(t) (i.e. the space of continuous conjugate linear maps V(t) → C) and using standard identifications one writes V(t) ⊂ H ⊂ V‘(t).

scholarly journals Algorithm for Solving a New System of Generalized Nonlinear Quasi-Variational-Like Inclusions in Hilbert Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Shamshad Husain ◽  
Sanjeev Gupta ◽  
Huma Sahper
Keyword(s):  
Exact Solutions ◽  
Existence Theorem ◽  
Hilbert Spaces ◽  
Iterative Algorithms ◽  
Approximate Solutions ◽  
Cocoercive Operator ◽  
New System

We introduce and study a new system of generalized nonlinear quasi-variational-like inclusions with H(·,·)-cocoercive operator in Hilbert spaces. We suggest and analyze a class of iterative algorithms for solving the system of generalized nonlinear quasi-variational-like inclusions. An existence theorem of solutions for the system of generalized nonlinear quasi-variational-like inclusions is proved under suitable assumptions which show that the approximate solutions obtained by proposed algorithms converge to the exact solutions.

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.

Approximate Controllability of Partial Fractional Neutral Integro-Differential Inclusions With Infinite Delay in Hilbert Spaces

2016 ◽  
Vol 11 (1) ◽  
Author(s):  
Zuomao Yan ◽  
Hongwu Zhang
Keyword(s):  
Hilbert Spaces ◽  
Differential Inclusions ◽  
Approximate Controllability ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Multivalued Operators ◽  
Approximately Controllable ◽  
Fractional System ◽  
The Fixed Point Theorem ◽  
Necessary And Sufficient

We study the approximate controllability of a class of fractional partial neutral integro-differential inclusions with infinite delay in Hilbert spaces. By using the analytic α-resolvent operator and the fixed point theorem for discontinuous multivalued operators due to Dhage, a new set of necessary and sufficient conditions are formulated which guarantee the approximate controllability of the nonlinear fractional system. The results are obtained under the assumption that the associated linear system is approximately controllable. An example is provided to illustrate the main results.

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