scholarly journals On first order differential inclusions with periodic boundary conditions

2005 ◽  
pp. 71-78
Author(s):  
Mouffak Benchohra ◽  
Sotiris K. Ntouyas
Keyword(s):  
Boundary Conditions ◽  
Differential Inclusions ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
First Order

scholarly journals Applications of Stieltjes Derivatives to Periodic Boundary Value Inclusions

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2142
Author(s):  
Bianca Satco ◽  
George Smyrlis
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Periodic Boundary Conditions ◽  
Solution Set ◽  
First Order

In the present paper, we are interested in studying first-order Stieltjes differential inclusions with periodic boundary conditions. Relying on recent results obtained by the authors in the single-valued case, the existence of regulated solutions is obtained via the multivalued Bohnenblust–Karlin fixed-point theorem and a result concerning the dependence on the data of the solution set is provided.

scholarly journals Stieltjes Differential Inclusions with Periodic Boundary Conditions without Upper Semicontinuity

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 55
Author(s):  
Valeria Marraffa ◽  
Bianca Satco
Keyword(s):  
Boundary Conditions ◽  
Differential Inclusions ◽  
Periodic Boundary ◽  
Existence Of Solutions ◽  
Compact Convex ◽  
Upper Semicontinuity ◽  
Periodic Boundary Conditions ◽  
Set Valued Mapping ◽  
Periodic Problems ◽  
The Right

We are studying first order differential inclusions with periodic boundary conditions where the Stieltjes derivative with respect to a left-continuous non-decreasing function replaces the classical derivative. The involved set-valued mapping is not assumed to have compact and convex values, nor to be upper semicontinuous concerning the second argument everywhere, as in other related works. A condition involving the contingent derivative relative to the non-decreasing function (recently introduced and applied to initial value problems by R.L. Pouso, I.M. Marquez Albes, and J. Rodriguez-Lopez) is imposed on the set where the upper semicontinuity and the assumption to have compact convex values fail. Based on previously obtained results for periodic problems in the single-valued cases, the existence of solutions is proven. It is also pointed out that the solution set is compact in the uniform convergence topology. In particular, the existence results are obtained for periodic impulsive differential inclusions (with multivalued impulsive maps and finite or possibly countable impulsive moments) without upper semicontinuity assumptions on the right-hand side, and also the existence of solutions is derived for dynamic inclusions on time scales with periodic boundary conditions.

scholarly journals Positive Periodic Solutions for First-Order Difference Equations with Impulses

2021 ◽  
Author(s):  
Mesliza Mohamed ◽  
Gafurjan Ibragimov ◽  
Seripah Awang Kechil
Keyword(s):  
Boundary Conditions ◽  
Periodic Solutions ◽  
Difference Equations ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Positive Periodic Solutions ◽  
Order Difference ◽  
First Order

This paper investigates the first-order impulsive difference equations with periodic boundary conditions

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