Existence of positive solutions for second-order nonlinear neutral dynamic equations on time scales

Author:

Bouchelaghem Faycal1,Ardjouni Abdelouaheb2,Djoudi Ahcene3

Affiliation:

1. High School of Management Sciences Annaba , Annaba 23000 , Algeria , Laboratory of Analysis and Control of Differential Equations ”ACED” , Fac. MISM, Dept. Maths, Univ 8 May 1945 Guelma , Guelma 24000 , Algeria .

2. Department of Mathematics and Informatics , Univ Souk Ahras , P.O. Box 1553, Souk Ahras 41000 , Algeria , Applied Mathematics Lab., Faculty of Sciences, Department of Mathematics , Univ Annaba , P.O. Box 12 , Annaba 23000 , Algeria

3. Applied Mathematics Lab ., Faculty of Sciences, Department of Mathematics , Univ Annaba , P.O. Box 12, Annaba 23000 , Algeria

Abstract

Abstract In this article we study the existence of positive solutions for second-order nonlinear neutral dynamic equations on time scales. The main tool employed here is Schauder’s fixed point theorem. The results obtained here extend the work of Culakova, Hanustiakova and Olach [12]. Two examples are also given to illustrate this work.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Control and Optimization,Numerical Analysis,Analysis

Reference16 articles.

1. [1] M. Adivar and Y. N. Raffoul, Existence of periodic solutions in totally nonlinear delay dynamic equations, Electronic Journal of Qualitative Theory of Differential Equations 2009(1) (2009), 1–20.

2. [2] A. Ardjouni, A. Djoudi, Existence of positive periodic solutions for nonlinear neutral dynamic equations with variable delay on a time scale, Malaya Journal of Matematik 2(1) (2013), 60–67.

3. [3] A. Ardjouni, A. Djoudi, Existence of periodic solutions for nonlinear neutral dynamic equations with functional delay on a time scale, Acta Univ. Palacki. Olomnc., Fac. rer. nat., Mathematica 52(1) (2013), 5–19.

4. [4] A. Ardjouni, A. Djoudi, Existence of periodic solutions for nonlinear neutral dynamic equations with variable delay on a time scale, Commun Nonlinear Sci Numer Simulat 17 (2012), 3061–3069.

5. [5] A. Ardjouni, A. Djoudi, Periodic solutions in totally nonlinear dynamic equations with functional delay on a time scale, Rend. Sem. Mat. Univ. Politec. Torino Vol. 68, 4(2010), 349-359.

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