Set of solutions of a differential inclusion in banach space. I

1984 ◽  
Vol 24 (6) ◽  
pp. 941-954 ◽  
Author(s):  
A. A. Tolstonogov ◽  
P. I. Chugunov
Keyword(s):  
Banach Space ◽  
Differential Inclusion

scholarly journals On Noncompact Fractional Order Differential Inclusions with Generalized Boundary Condition and Impulses in a Banach Space

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Irene Benedetti ◽  
Valeri Obukhovskii ◽  
Valentina Taddei
Keyword(s):  
Banach Space ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Nonlinear Term ◽  
Reflexive Banach Space ◽  
Nonlocal Conditions ◽  
Existence Results ◽  
Fractional Differential ◽  
Partial Differential Inclusion ◽  
Generalized Boundary Condition

We provide existence results for a fractional differential inclusion with nonlocal conditions and impulses in a reflexive Banach space. We apply a technique based on weak topology to avoid any kind of compactness assumption on the nonlinear term. As an example we consider a problem in population dynamic described by an integro-partial-differential inclusion.

On a fractional differential inclusion with integral boundary conditions in Banach space

2013 ◽  
Vol 16 (3) ◽  
Author(s):  
Phan Phung ◽  
Le Truong
Keyword(s):  
Banach Space ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Fractional Derivative ◽  
Differential Inclusion ◽  
Integral Boundary Conditions ◽  
Young Measures ◽  
Integral Boundary ◽  
Liouville Fractional Derivative ◽  
Fractional Differential

AbstractWe consider a class of boundary value problem in a separable Banach space E, involving a nonlinear differential inclusion of fractional order with integral boundary conditions, of the form (*)$\left\{ \begin{gathered} D^\alpha u(t) \in F(t,u(t),D^{\alpha - 1} u(t)),a.e.,t \in [0,1], \hfill \\ I^\beta u(t)|_{t = 0} = 0,u(1) = \int\limits_0^1 {u(t)dt,} \hfill \\ \end{gathered} \right. $ where D α is the standard Riemann-Liouville fractional derivative, F is a closed valued mapping. Under suitable conditions we prove that the solutions set of (*) is nonempty and is a retract in W Eα,1(I). An application in control theory is also provided by using the Young measures.

scholarly journals Abstract-valued Orlicz spaces of range-varying type

2018 ◽  
Vol 16 (1) ◽  
pp. 924-954 ◽  
Author(s):  
Qinghua Zhang
Keyword(s):  
Banach Space ◽  
Elliptic Equation ◽  
Differential Inclusion ◽  
Sobolev Spaces ◽  
Nonlinear Elliptic Equation ◽  
Orlicz Spaces ◽  
Convex Functional ◽  
Geometrical Properties ◽  
Nonstandard Growth ◽  
Nonlinear Elliptic

AbstractThis paper mainly deals with the abstract-valued Orlicz spaces of range-varying type. Using notions of Banach space net and continuous modular net etc., we give definitions of Lϱθ(⋅)(I, Xθ(⋅)) and $\begin{array}{} L_{+}^{\varrho_{\theta(\cdot)}} \end{array} $(I, Xθ(⋅)), and discuss their geometrical properties as well as the representation of $\begin{array}{} L_{+}^{\varrho_{\theta(\cdot)}} \end{array} $(I, Xθ(⋅))*. We also investigate some functionals and operators on Lϱθ(⋅)(I, Xθ(⋅)), giving expression for the subdifferential of the convex functional generated by another continuous modular net. After making some investigations on the Bochner-Sobolev spaces W1, ϱθ(⋅)(I, Xθ(⋅)) and $\begin{array}{} W_{\textrm{per}}^{1,\varrho_{\theta(\cdot)}} \end{array} $(I, Xθ(⋅)), and the intersection space $\begin{array}{} W_{\textrm{per}}^{1,\varrho_{\theta(\cdot)}} \end{array} $(I, Xθ(⋅)) ∩ Lφϑ(⋅)(I, Vϑ(⋅)), a second order differential inclusion together with an anisotropic nonlinear elliptic equation with nonstandard growth are also taken into account.

scholarly journals BLURRED MAXIMAL CYCLICALLY MONOTONE SETS AND BIPOTENTIALS

2010 ◽  
Vol 08 (04) ◽  
pp. 323-336 ◽  
Author(s):  
MARIUS BULIGA ◽  
GÉRY DE SAXCÉ ◽  
CLAUDE VALLÉE
Keyword(s):  
Banach Space ◽  
Differential Inclusion ◽  
Reflexive Banach Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

Let X be a reflexive Banach space and Y its dual. In this paper, we find necessary and sufficient conditions for the existence of a bipotential for a blurred maximal cyclically monotone set. Equivalently, we find a necessary and sufficient condition on ϕ ∈ Γ0(X) so that the differential inclusion [Formula: see text] can be put in the form y ∈ ∂b(·, y)(x), with b a bipotential.

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