Pseudo Almost Periodic Solutions for a Class of Fourth-Order Nonlinear Differential Equations with a Deviating Argument

详细信息    查看全文

• 作者：Farouk Chérif
• 关键词：Nonlinear ordinary differential equation ; Global stability ; Pseudo almost periodic
• 刊名：Differential Equations and Dynamical Systems
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：24
• 期：1
• 页码：81-97
• 全文大小：435 KB
• 参考文献：1.Agarwal, R.P., Graceb, S.R., Manojlovicc, J.V.: Oscillation criteria for certain fourth order nonlinear functional differential equations. Math. Comput. Model. 44, 163–187 (2006)CrossRef MATH
  2.Amerio, L., Prouse, G.: Almost-Periodic Functions and Functional Analysis. Von Nostrand Reinhold Co., New York (1971)CrossRef
  3.Ammar, B., Chérif, F., Alimi, A.M.: Existence and uniqueness of pseudo almost-periodic solutions of recurrent neural networks with time-varying coefficients and mixed delays. IEEE Transactions on neural networks and learning systems 23(1), 109–118 (2012)CrossRef
  4.Amster, P., Mariani, M.C.: Oscillating solutions of a nonlinear fourth order ordinary differential equation. J. Math. Anal. Appl. 325, 1133–1141 (2007)CrossRef MathSciNet MATH
  5.Carriao, P.C., Faria, L.F.O., Miyagaki, O.H.: Periodic solutions for extended Fisher–Kolmogorov and Swift–Hohenberg equations by truncature techniques. Non-linear Anal. 67, 3076–3083 (2007)CrossRef MathSciNet MATH
  6.Chérif, F.: A various types of almost periodic functions on Banach spaces. Int. Math. Forum 6(20), 953–985 (2011)MathSciNet MATH
  7.Cronin, J.: Some mathematics of biological oscillations. SIAM Rev. 19, 100–137 (1977)CrossRef MathSciNet MATH
  8.Everitt, W.N., Markett, C., Littlejohn, L.L.: Properties of the solutions of the fourth-order Bessel-type differential equation. J. Math. Anal. Appl. 359, 252–264 (2009)CrossRef MathSciNet MATH
  9.Fink, A.M.: Almost Periodic Differential Equations. Springer, Berlin (1974)MATH
  10.N’Guérékata, G.M.: Topics in Almost Automorphy. Springer, New York (2005)MATH
  11.Jin, S., Lu, S.: Periodic solutions for a fourth order p-Laplacian differential equation with a deviating argument. Nonlinear Anal. 69, 1710–1718 (2008)CrossRef MathSciNet MATH
  12.Li, F., Li, Y.Z., Liang, Z.: Existence and multiplicity of solutions to 2mth-order ordinarydifferential equations. J. Math. Anal. Appl. 331, 958–977 (2007)CrossRef MathSciNet MATH
  13.Li, B.: Uniqueness and stability of a limit cycle for a third-order dynamical system arising in neuron modeling. Nonlinear Anal. 5, 13–19 (1981)CrossRef MathSciNet MATH
  14.Mawhin, J., Zanolin, F.: A continuation approach to fourth order superlinear periodic boundary value problems. Topol. Methods Nonlinear Anal. 2, 55–74 (1993)MathSciNet MATH
  15.Peletier, L.A., Troy, W.C.: Spatial patterns described by the Fisher-Kolmogorov equation: periodic solutions. SIAM J. Math. Anal. 28, 1317–1353 (1997)CrossRef MathSciNet MATH
  16.Xiong, W., Yueb, G.: Almost periodic solutions for a class of fourth-order nonlinear differential equations with a deviating argument. Comput. Math. Appl. 60, 1184–1190 (2010)CrossRef MathSciNet MATH
  17.Yao, Q.: Existence, multiplicity and infinite solvability of positive solutions to a nonlinear fourth-order periodic boundary value problem. Nonlinear Anal. 63, 237–246 (2005)CrossRef MathSciNet MATH
  18.Zhang, C.: Pseudo almost periodic functions and their applications. Ph.D. thesis, University of Western Ontario (1992)
  19.Zhang, C.: Almost Periodic Type Functions and Ergodicity. Kluwer Academic Publishers and Science Press, Beijing (2003)CrossRef MATH
  20.Tomoshenko, S., Gere, S.: Theory of Elastic Stability, 2nd edn. McGraw Hill, New York (1961)
  
• 作者单位：Farouk Chérif (1)
  
  1. ISSATs and Laboratory of Mathematical Physic, Specials Functions and Applications, LR11ES35, Ecole Supérieure des Sciences et de Technologie de Hammam-Sousse, Université de Sousse, Sousse, Tunisia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  
• 出版者：Springer India
• ISSN：0974-6870

文摘

This work is concerned with a class of fourth order semilinear ordinary differential equation with pseudo almost periodic environment and multiple delays. Specifically, we establish the existence and uniqueness of the pseudo almost periodic solutions. Furthermore, we discuss the global stability of the considered equation. Keywords Nonlinear ordinary differential equation Global stability Pseudo almost periodic