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Existence Results for First and Second Order Nonconvex Sweeping Processes with Perturbations and with Delay: Fixed Point Approach
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Messaoud Bounkhel
Veröffentlicht/Copyright:
10. März 2010
Abstract
We are interested in existence results for nonconvex functional differential inclusions. First, we prove an existence result, in separable Hilbert spaces, for first order nonconvex sweeping processes with perturbation and with delay. Then, by using this result and a fixed point theorem we prove an existence result for second order nonconvex sweeping processes with perturbation and with delay of the form 𝑢˙ (𝑡) ∈ 𝐶(𝑢(𝑡)), 𝑢¨(𝑡) ∈ –𝑁𝑃(𝐶(𝑢(𝑡)); 𝑢˙(𝑡)) + 𝐹(𝑡, 𝑢˙𝑡) when 𝐶 is a nonconvex bounded Lipschitz set-valued mapping and 𝐹 is a set-valued mapping with convex compact values taking their values in finite dimensional spaces.
Key words and phrases:: Uniformly prox-regular set; nonconvex sweeping processes; delay; differential inclusions
Received: 2005-03-16
Published Online: 2010-03-10
Published in Print: 2006-June
© Heldermann Verlag
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- Existence Theory for Perturbed Nonlinear Boundary Value Problems with Integral Boundary Conditions
- A Generalization of Bihari's Lemma for Discontinuous Functions and Its Application to the Stability Problem of Differential Equations with Impulse Disturbance
- Existence Results for First and Second Order Nonconvex Sweeping Processes with Perturbations and with Delay: Fixed Point Approach
- The Potential Method for the Reactance Wave Diffraction Problem in a Scale of Spaces
- On the Continuity of the Nemytskij Operator between the Spaces 𝐿𝑝1(𝑋) and 𝐿𝑝2(𝑋)
- Monadic 𝐵𝐿-Algebras
- Rate of Approximation for Certain Durrmeyer Operators
- On Decompositions of a Cube into Cubes and Simplexes
- A Positive Answer to Velichko's Question
- An Inverse Result in Simultaneous Approximation by Modified Beta Operators
- Weyl's Theorem for Algebraically (𝑝, 𝑘)-Quasihyponormal Operators
- Modulus of Continuity and Best Approximation with Respect to Vilenkin-Like Systems in Some Function Spaces
- Exact Distributions of the Product and Ratio of Absolute Values of Pearson Type VII and Bessel Function Random Variables
- An Automatically Stable and Order Three Split Rational Approximation of a Semigroup
- Selfadjoint Operators and Generalized Central Algorithms in Frechet Spaces
- Oscillation Theorems for Certain Even Order Delay Differential Equations Involving General Means
- Corrections to “On a Singular Direction of a Meromorphic Function”
Schlagwörter für diesen Artikel
Uniformly prox-regular set;
nonconvex sweeping processes;
delay;
differential inclusions
Artikel in diesem Heft
- Semimartingale Local Time and the American Put Option
- Existence Theory for Perturbed Nonlinear Boundary Value Problems with Integral Boundary Conditions
- A Generalization of Bihari's Lemma for Discontinuous Functions and Its Application to the Stability Problem of Differential Equations with Impulse Disturbance
- Existence Results for First and Second Order Nonconvex Sweeping Processes with Perturbations and with Delay: Fixed Point Approach
- The Potential Method for the Reactance Wave Diffraction Problem in a Scale of Spaces
- On the Continuity of the Nemytskij Operator between the Spaces 𝐿𝑝1(𝑋) and 𝐿𝑝2(𝑋)
- Monadic 𝐵𝐿-Algebras
- Rate of Approximation for Certain Durrmeyer Operators
- On Decompositions of a Cube into Cubes and Simplexes
- A Positive Answer to Velichko's Question
- An Inverse Result in Simultaneous Approximation by Modified Beta Operators
- Weyl's Theorem for Algebraically (𝑝, 𝑘)-Quasihyponormal Operators
- Modulus of Continuity and Best Approximation with Respect to Vilenkin-Like Systems in Some Function Spaces
- Exact Distributions of the Product and Ratio of Absolute Values of Pearson Type VII and Bessel Function Random Variables
- An Automatically Stable and Order Three Split Rational Approximation of a Semigroup
- Selfadjoint Operators and Generalized Central Algorithms in Frechet Spaces
- Oscillation Theorems for Certain Even Order Delay Differential Equations Involving General Means
- Corrections to “On a Singular Direction of a Meromorphic Function”
