On the existence of positive periodic solutions for totally nonlinear neutral differential equations of the second-order with functional delay

• Autorzy: Essel E. K. , Yankson E.

Identyfikatory

DOI

http://dx.doi.org/10.7494/OpMath.2014.34.3.469

• Języki publikacji: EN

Abstrakty

EN

We prove that the totally nonlinear second-order neutral differential equation [formula] has positive periodic solutions by employing the Krasnoselskii-Burton hybrid fixed point theorem.

Słowa kluczowe

EN

Krasnoselskii; neutral; positive periodic solution

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2014
• Tom: Vol. 34, no. 3
• Strony: 469--481
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Essel E. K.

• University of Cape Coast Department of Mathematics and Statistics Cape Coast, Ghana

autor

Yankson E.

• University of Cape Coast Department of Mathematics and Statistics Cape Coast, Ghana

Bibliografia

• [1] M. Adivar, M.N. Islam, Y.N. Raffoul, Separate contraction and existence of periodic solutions in totally nonlinear delay differential equations, Hacettepe Journal of Mathematics and Statistics 41 (2012), 1–13.
• [2] A. Ardjouni, A. Djoudi, Existence of periodic solutions for a second order nonlinear neutral differential equation with functional delay, Elect. Journal of Qual. Theory of Diff. Equ. 31 (2012), 1–9.
• [3] T.A. Burton, Stability by Fixed Point Theory for Functional Differential Equations, Dover Publications, New York, 2006.
• [4] F.D. Chen, Positive periodic solutions of neutral Lotka-Volterra system with feedback control, Appl. Math. Comput. 162 (2005) 3, 1279–1302.
• [5] F.D. Chen, J.L. Shi, Periodicity in a nonlinear predator-prey system with state dependent delays, Acta Math. Appl. Sin. Engl. Ser. 21 (2005) 1, 49–60.
• [6] W. Cheung, J. Ren, W. Han, Positive periodic solutions for second-order differential equations with generalized neutral operator, The Australian Journal of Mathematical Analysis and Applications 6 (2009), 1–16.
• [7] Y.M. Dib, M.R. Maroun, Y.N. Raffoul, Periodicity and stability in neutral nonlinear differential equations with functional delay, Electron. J. Differ. Equ. 142 (2005), 1–11.
• [8] M. Fan, K. Wang, P.J.Y. Wong, R.P. Agarwal, Periodicity and stability in periodic n-species Lotka-Volterra competition system with feedback controls and deviating arguments, Acta Math. Sin. Engl. Ser. 19 (2003) 4, 801–822.
• [9] E.R. Kaufmann, Y.N. Raffoul, Periodic solutions for a neutral nonlinear dynamical equation on a time scale, J. Math. Anal. Appl. 319 (2006) 1, 315–325.
• [10] E.R. Kaufmann, Y.N. Raffoul, Periodicity and stability in neutral nonlinear dynamic equations with functional delay on a time scale, Electron. J. Differ. Equ. 27 (2007), 1–12.
• [11] E.R. Kaufmann, A nonlinear neutral periodic differential equation, Electron. J. Differ. Equ. 88 (2010), 1–8.
• [12] W.T. Li, L.L. Wang, Existence and global attractively of positive periodic solutions of functional differential equations with feedback control, J. Comput. App. Math. 180 (2005), 293–309.
• [13] Y. Liu, W. Ge, Positive periodic solutions of nonlinear duffing equations with delay and variable coefficients, Tamsui Oxf. J. Math. Sci. 20 (2004), 235–255.
• [14] Y.N. Raffoul, Periodic solutions for neutral nonlinear differential equations with functional delay, Electron. J. Differ. Equ. 102 (2003), 1–7.
• [15] Y.N. , Stability in neutral nonlinear differential equations with functional delays using fixed-point theory, Math. Comput. Modelling 40 (2004) 7–8, 691–700.
• [16] Y.N. Raffoul, Positive periodic solutions in neutral nonlinear differential equations, E.J. Qualitative Theory of Diff. Equ. 16 (2007), 1–10.
• [17] D.R. Smart, Fixed point theorems, Cambridge Tracts in Mathematics, No. 66. Cambridge University Press, London-New York, 1974.
• [18] H.Y.Wang, Positive periodic solutions of functional differential equations, J. Differential Equations 202 (2004), 354–366.
• [19] Y. Wang, H. Lian, W. Ge, Periodic solutions for a second order nonlinear functional differential equation, Applied Mathematics Letters 20 (2007), 110–115.
• [20] E. Yankson, Positive periodic solutions for second-order neutral differential equations with functional delay, Electron. J. Differ. Equ. 14 (2012), 1–6.
• [21] E. Yankson, Existence of periodic solutions for totally nonlinear neutral differential equations with functional delay, Opuscula Math. 32 (2012) 3, 617–627