An Existence Result for Discontinuous Second-Order Nonconvex State-Dependent Sweeping Processes

2017 ◽  
Vol 79 (2) ◽  
pp. 515-546 ◽  
Author(s):  
S. Adly ◽  
F. Nacry
Keyword(s):  
Existence Result ◽  
Second Order ◽  
State Dependent ◽  
Sweeping Processes

Existence Results for First and Second Order Nonconvex Sweeping Processes with Perturbations and with Delay: Fixed Point Approach

2006 ◽  
Vol 13 (2) ◽  
pp. 239-249
Author(s):  
Messaoud Bounkhel
Keyword(s):  
Fixed Point ◽  
Existence Result ◽  
Existence Results ◽  
Second Order ◽  
Convex Compact ◽  
Set Valued Mapping ◽  
Finite Dimensional ◽  
Sweeping Processes ◽  
Functional Differential ◽  
Nonconvex Functional

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.

scholarly journals Existence Results for Second Order Nonconvex Sweeping Processes in q-Uniformly Convex and 2-Uniformly Smooth Separable Banach Spaces

Symmetry ◽  
2018 ◽  
Vol 11 (1) ◽  
pp. 28
Author(s):  
Djalel Bounekhel ◽  
Messaoud Bounkhel ◽  
Mostafa Bachar
Keyword(s):  
Banach Spaces ◽  
Differential Inclusions ◽  
Existence Result ◽  
Lipschitz Continuity ◽  
Second Order ◽  
Uniformly Convex ◽  
Set Valued Mapping ◽  
Uniformly Smooth ◽  
Sweeping Processes ◽  
Regular Sets

We prove an existence result, in the separable Banach spaces setting, for second order differential inclusions of type sweeping process. This type of differential inclusion is defined in terms of normal cones and it covers many dynamic quasi-variational inequalities. In the present paper, we prove in the nonconvex case an existence result of this type of differential inclusions when the separable Banach space is assumed to be q-uniformly convex and 2-uniformly smooth. In our proofs we use recent results on uniformly generalized prox-regular sets. Part of the novelty of the paper is the use of the usual Lipschitz continuity of the set-valued mapping which is very easy to verify contrarily to the ones used in the previous works. An example is stated at the end of the paper, showing the application of our existence result.

scholarly journals Approximate controllability of second order impulsive systems with state-dependent delay in banach spaces

2019 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Soniya Singh ◽  
◽  
Sumit Arora ◽  
Manil T. Mohan ◽  
Jaydev Dabas ◽  
...  
Keyword(s):  
Banach Spaces ◽  
Approximate Controllability ◽  
Second Order ◽  
Impulsive Systems ◽  
State Dependent ◽  
State Dependent Delay

Reduction approach to second order perturbed state-dependent sweeping process

2019 ◽  
Vol 28 (2) ◽  
Author(s):  
MUSTAPHA FATEH YAROU
Keyword(s):  
Fixed Point Theory ◽  
Point Theory ◽  
Second Order ◽  
Sweeping Process ◽  
New Approach ◽  
Standard Methods ◽  
First Order ◽  
Finite Dimensional ◽  
Perturbed State ◽  
State Dependent

In this paper, we present a new approach to solving second order nonconvex perturbed sweeping process in finite dimensional setting. It consists in a reduction of the problem to a first order one without use of the standard methods of fixed point theory. The perturbation, that is the external force applied on the system is not necessary with bounded values.

Linear second order elliptic equations with Venttsel boundary conditions

1991 ◽  
Vol 118 (3-4) ◽  
pp. 193-207 ◽  
Author(s):  
Yousong Luo ◽  
Neil S. Trudinger
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Elliptic Equations ◽  
Existence Result ◽  
Boundary Value ◽  
Second Order ◽  
Classical Solutions ◽  
Schauder Estimate ◽  
Second Order Elliptic Equations

SynopsisWe prove a Schauder estimate for solutions of linear second order elliptic equations with linear Venttsel boundary conditions, and establish an existence result for classical solutions for such boundary value problems.

On second order differential equations with state-dependent delay

2017 ◽  
Vol 97 (15) ◽  
pp. 2610-2617 ◽  
Author(s):  
Eduardo Hernández ◽  
Katia A. G. Azevedo ◽  
Donal O’Regan
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Second Order Differential Equations ◽  
State Dependent ◽  
State Dependent Delay
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