scholarly journals An existence theorem for differential inclusions on Banach space

1992 ◽  
Vol 5 (2) ◽  
pp. 123-129 ◽  
Author(s):  
N. U. Ahmed
Keyword(s):  
Banach Space ◽  
Control Theory ◽  
Large Class ◽  
Existence Theorem ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Nonlinear Differential Inclusions

In this paper we consider the question of existence of solutions for a large class of nonlinear differential inclusions on Banach space arising from control theory.

On the Carathéodory superposition of multifunctions and an existence theorem

2014 ◽  
Vol 64 (2) ◽  
Author(s):  
Grażyna Kwiecińska
Keyword(s):  
Banach Space ◽  
Continuous Function ◽  
Existence Theorem ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Reflexive Banach Space

AbstractLet I ⊂ ℝ be an interval and Y a reflexive Banach space. We introduce the (H) property of a multifunction F from I × Y to Y and prove that the Carathéodory superposition of F with each continuous function f from I to Y is a derivative provided that F has the (H) property. Some application of this theorem to the existence of solutions of differential inclusions f′(x) ∈ F(x, f(x)) is given.

scholarly journals Existence Results for Differential Inclusions with Nonlinear Growth Conditions in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Messaoud Bounkhel
Keyword(s):  
Banach Space ◽  
Hilbert Spaces ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Growth Conditions ◽  
Existence Results ◽  
Nonlinear Growth ◽  
Upper Semicontinuous ◽  
Set Valued Mapping ◽  
Sweeping Processes

In the Banach space setting, the existence of viable solutions for differential inclusions with nonlinear growth; that is,ẋ(t)∈F(t,x(t))a.e. onI,x(t)∈S,∀t∈I,x(0)=x0∈S, (*), whereSis a closed subset in a Banach space𝕏,I=[0,T],(T>0),F:I×S→𝕏, is an upper semicontinuous set-valued mapping with convex values satisfyingF(t,x)⊂c(t)x+xp𝒦,∀(t,x)∈I×S, wherep∈ℝ, withp≠1, andc∈C([0,T],ℝ+). The existence of solutions for nonconvex sweeping processes with perturbations with nonlinear growth is also proved in separable Hilbert spaces.

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.

Near viability for fully nonlinear differential inclusions

2014 ◽  
Vol 12 (10) ◽  
Author(s):  
Irina Căpraru ◽  
Alina Lazu
Keyword(s):  
Differential Inclusion ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Null Controllability ◽  
Dissipative Operator ◽  
Nonlinear Case ◽  
Tangency Condition ◽  
Gronwall’S Lemma ◽  
Nonlinear Differential Inclusions ◽  
Near Viability

AbstractWe consider the nonlinear differential inclusion x′(t) ∈ Ax(t) + F(x(t)), where A is an m-dissipative operator on a separable Banach space X and F is a multi-function. We establish a viability result under Lipschitz hypothesis on F, that consists in proving the existence of solutions of the differential inclusion above, starting from a given set, which remain arbitrarily close to that set, if a tangency condition holds. To this end, we establish a kind of set-valued Gronwall’s lemma and a compactness theorem, which are extensions to the nonlinear case of similar results for semilinear differential inclusions. As an application, we give an approximate null controllability result.

scholarly journals Local bounds and existence of solutions to non-convex differential inclusions

2009 ◽  
Vol 42 (1) ◽  
Author(s):  
Stanisław Domachowski
Keyword(s):  
Existence Theorem ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Global Bifurcation ◽  
Continuous Mapping ◽  
Bifurcation Theorem ◽  
Completely Continuous

AbstractUsing a global bifurcation theorem for convex-valued completely continuous mapping we prove an existence theorem for differential inclusions of the form

Existence of solutions for Riemann–Liouville multi-valued fractional boundary value problems

2017 ◽  
Vol 24 (4) ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris K. Ntouyas
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Differential Inclusions ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Fractional Differential Inclusions ◽  
Fractional Differential ◽  
Fractional Boundary Conditions ◽  
Fractional Boundary Value Problems

AbstractIn this paper, we study a class of Riemann–Liouville fractional differential inclusions with fractional boundary conditions. By using standard fixed point theorems, we obtain some new existence results for convex as well as nonconvex multi-valued mappings in an appropriate Banach space. The obtained results are illustrated by examples.

scholarly journals On The Existence of Solutions for Nonlinear Differential Inclusions

2015 ◽  
Vol 61 (1) ◽  
pp. 195-208 ◽  
Author(s):  
Irina Căpraru ◽  
Aurelian Cernea
Keyword(s):  
Cauchy Problem ◽  
Banach Spaces ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Nonlinear Differential Inclusions ◽  
Filippov Type

Abstract We consider a Cauchy problem for a nonlinear differential inclusion in separable and nonseparable Banach spaces under Filippov type assumptions and several existence results are obtained.

scholarly journals Existence of Solutions for Fractional Differential Inclusions with Separated Boundary Conditions in Banach Space

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Mabrouk Bragdi ◽  
Amar Debbouche ◽  
Dumitru Baleanu
Keyword(s):  
Banach Space ◽  
Differential Inclusions ◽  
Existence Result ◽  
Existence Of Solutions ◽  
Necessary Conditions ◽  
Fractional Differential Inclusions ◽  
Separated Boundary Conditions ◽  
Fractional Differential ◽  
Fixed Point Technique ◽  
Fractional Orders

We discuss the existence of solutions for a class of some separated boundary differential inclusions of fractional orders2<α<3involving the Caputo derivative. In order to obtain necessary conditions for the existence result, we apply the fixed point technique, fractional calculus, and multivalued analysis.

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