Mathématiques
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Item THE EXISTENCE OF PERIODIC SOLUTIONS OF A SECOND ORDER ITERATIVE DIFFERENTIAL EQUATION(Acta Math. Univ. Comenianae Vol. XCII, 1 , pp. 9{22, 2023) KHEMIS ,R; BOUAKKAZ , A; CHOUAF , SIn this work, we consider a class of second order iterative di erential equations. Using Schauder's xed point theorem and the Green's functions method, the existence of periodic solutions is proved after establishing the equivalence of our problem with a certain integral equation. Finally, we end this article with a simple conclusion recapitulating the guiding idea of our approach. Obtained ndings complement some previous publications in the literature.Item EXPONENTIAL STABILITY FOR A NONLINEAR TIMOSHENKO SYSTEM WITH DISTRIBUTED DELAY(International Journal of Analysis and Applications Volume 19, Number 1 , 77-90, 2021) BOUZETTOUTA , Lamine; HEBHOUB , Fahima ; GHENNAM , Karima; BENFERDI , SabrinaThis paper is concerned with a nonlinear Timoshenko system modeling clamped thin elastic beams with distributed delay time. The distributed delay is de ned on feedback term associated to the equation for rotation angle. Under suitable assumptions on the data, we establish the exponential stability of the system under the usual equal wave speeds assumption.Item Existence, uniqueness and stability results of an iterative survival model of red blood cells with a delayed nonlinear harvesting term(Journal of Mathematical Modeling Vol. 10, No. 3, pp. 515-528, 2022) Khemis , Marwa ; Bouakkaz , Ahlème; Khemis , RabahIn this article, a first-order iterative Lasota–Wazewska model with a nonlinear delayed harvesting term is discussed. Some sufficient conditions are derived for proving the existence, uniqueness and continuous dependence on parameters of positive periodic solutions with the help of Krasnoselskii’s and Banach fixed point theorems along with the Green’s functions method. Besides, at the end of this work, three examples are provided to show the accuracy of the conditions of our theoretical findings which are completely innovative and complementary to some earlier publications in the literatureItem THE EXISTENCE RESULT OF RENORMALIZED SOLUTION FOR NONLINEAR PARABOLIC SYSTEM WITH VARIABLE EXPONENT AND L1 DATA(International Journal of Analysis and Applications Volume 18, Number 5 , 748-773, 2020) SOUILAH , Fairouz; MAOUNI , Messaoud; SLIMANI , KamelIn this paper, we prove the existence result of a renormalized solution to a class of nonlinear parabolic systems, which has a variable exponent Laplacian term and a Leary lions operator with data belong to L1.Item Existence, uniqueness and stability of solutions to a delay hematopoiesis model(Journal of Innovative Applied Mathematics and Computational Sciences , 2(2) , 23–30, 2022) Bouakkaz , Ahlème; Khemis , RabahThis work aims to investigate a delay hematopoiesis model where the delay depends on both the time and the current density of mature blood cells. Based on the Banach contraction principle, the Schauder’s fixed point theorem and some properties of a Green’s function, we establish several interesting existence and uniqueness results of positive periodic solutions for the proposed model. The derived results are new and generalize some previous studies. Keywords: Fixed point theorem, Green’s function, Mackey–Glass equation, Periodic solution, Positive solution.Item Positive periodic solutions for a class of second-order differential equations with state-dependent delays(Turkish Journal of Mathematics , 1412 – 1426, 2020) BOUAKKAZ , Ahlème; KHEMIS , RabahIn this paper, we consider a class of second order differential equations with iterative source term. The main results are obtained by virtue of a Krasnoselskii fixed point theorem and some useful properties of a Green’s function which allows us to prove the existence of positive periodic solutions. Finally, an example is included to illustrate the correctness of our results.Item New results on periodic solutions for a nonlinear fourth-order iterative differential equation(Journal of Prime Research in Mathematics, 18(2) , 88–99, 2022) Khemis , Rabah; Bouakkaz , AhlèmeThe key task of this paper is to investigate a nonlinear fourth-order delay differential equation. By virtue of the fixed point theory and the Green’s functions method, we establish some new results on the existence, uniqueness and continuous dependence on parameters of periodic solutions. In addition, an example is given to corroborate the validity of our main results. Up to now, no work has been carried out on this topic. So, the findings of this paper are new and complement the available works in the literature to some degree.Item TOPOLOGICAL DEGREE METHOD FOR FRACTIONAL LAPLACIAN SYSTEM(Bulletin of Mathematical Analysis and Applications Volume 13 Issue 2, Pages10-19 , 2021) ABADA , Esma; LAKHAL , Hakim; MAOUNI , MessaoudIn this paper, we study the existence of weak solutions for a semilinear fractional elliptic system with Dirichlet boundary conditions. We apply the Leray-Schauder degree method in order to obtain a result about the existence of solutions.Item Existence and uniqueness of the weak solution for Keller-Segel model coupled with Boussinesq equations(Demonstratio Mathematica 2021; 54: 558–575, 2021) Lamine Bouzettouta; Amar Guesmia; Slimani , AliKeller-Segel chemotaxis model is described by a system of nonlinear partial differential equations: a convection diffusion equation for the cell density coupled with a reaction-diffusion equation for chemoattractant concentration. In this work, we study the phenomenon of Keller-Segel model coupled with Boussinesq equations. The main objective of this work is to study the global existence and uniqueness and boundedness of the weak solution for the problem, which is carried out by the Galerkin method