Instability to differential equations of fourth order with a variable deviating argument

• Autorzy: Tunҫ C.

Identyfikatory

DOI

10.7862/rf.2013.10

• Języki publikacji: EN

Abstrakty

EN

The main purpose of this paper is to give two instability theorems to fourth order nonlinear differential equations with a variable deviating argument.

Słowa kluczowe

EN

instability; Krasovskii criteria; differential equation; fourth order; deviating argument

PL

niestabilność; równanie różniczkowe; równanie różniczkowe czwartego rzędu

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2013
• Tom: Vol. 36
• Strony: 113--120
• Opis fizyczny: Bibliogr. 20 poz.

Twórcy

autor

Tunҫ C.

• Department of Mathematics, Faculty of Sciences, Yüzüncü Yıl University, 65080, Van, Turkey

Bibliografia

• [1] H. H. Dong and Y. F. Zhang, Instability of some nonlinear systems of third and fourth orders (Chinese), J. Luoyang Univ. 14 (1999), no. 4, 11-14.
• [2] L. È. Èl'sgol'ts, Introduction to the theory of differential equations with deviating arguments. Translated from the Russian by Robert J. McLaughlin Holden-Day, Inc., San Francisco, Calif.-London-Amsterdam, 1966.
• [3] J. O. C. Ezeilo, An instability theorem for a certain fourth order differential equation, Bull. London Math. Soc. 10 (1978), no. 2, 184-185.
• [4] J. O. C. Ezeilo, Extension of certain instability theorems for some fourth and fifth order differential equations, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 66(1979), no. 4, 239-242.
• [5] J. O. C. Ezeilo, Further instability theorems for some fourth order differential equations, J. Nigerian Math. Soc. 19 (2000), 1-7.
• [6] N. N.Krasovskii, Stability of motion. Applications of Lyapunov's second method to differential systems and equations with delay. Translated by J. L. Brenner Stanford University Press, Stanford, Calif. 1963.
• [7] J. LaSalle and S. Lefschetz, Stability by Liapunov's direct method, with applications. Mathematics in Science and Engineering, Vol. 4, Academic Press, New York-London 1961.
• [8] W. Li and K. Duan, Instability theorems for some nonlinear differential systems of fifth order, J. Xinjiang Univ. Natur. Sci. 17 (2000), no. 3, 1-5.
• [9] W. J. Li and Y. H. Yu, Instability theorems for some fourth-order and fifth-order differential equations (Chinese), J. Xinjiang Univ. Natur. Sci., 7 (1990), no. 2, 7-10.
• [10] D. E. Lu and Z. H. Liao, Instability of solution for the fourth order linear differential equation with varied coecient, Appl. Math. Mech. (English Ed.) 14 (1993), no. 5, 481-497; translated from Appl. Math. Mech. 14 (1993), no. 5, 455{469 (Chinese).
• [11] A. I. Sadek, Instability results for certain systems of fourth and fifth order differential equations, Appl. Math. Comput. 145 (2003), no. 2-3, 541-549.
• [12] W. A. Skrapek, Instability results for fourth-order differential equations, Proc. Roy. Soc. Edinburgh Sect. A 85 (1980), no. 3-4, 247-250.
• [13] W. J. Sun and X. Hou, New results about instability of some fourth and fth order nonlinear systems (Chinese), J. Xinjiang Univ. Natur. Sci.16 (1999), no. 4, 14-17.
• [14] A. Tiryaki, Extension of an instability theorem for a certain fourth order differential equation, Bull. Inst. Math. Acad. Sinica 16 (1988), no. 2, 163-165.
• [15] C. Tunҫ, An instability theorem for a certain vector differential equation of the fourth order, JIPAM. J. Inequal. Pure Appl. Math. 5 (2004), no. 1, Article 5, 5 pp. (electronic).
• [16] C. Tunҫ, A further instability result for a certain vector differential equation of fourth order, Int. J. Math. Game Theory Algebra 15 (2006), no. 5, 489-495.
• [17] C. Tunҫ, Instability of solutions for certain nonlinear vector differential equations of fourth order, Neliniini Koliv. 12 (2009), no. 1, 120{129; translation in Nonlinear Oscil.(N. Y.) 12 (2009), no. 1, 123-132.
• [18] C. Tunҫ, On the instability of solutions of a nonlinear vector differential equation of fourth order, Ann. Di erential Equations 27 (2011), no. 4, 418-421.
• [19] C. Tunҫ, On the instability of solutions of nonlinear delay differential equations of fourth and fth order, Sains Malaysiana 40 (12), (2011), 1455-1459.
• [20] C. Tunҫ and E. Tunҫ, A result on the instability of solutions of certain non-autonomous vector differential equations of fourth order, East-West J. Math. 6 (2004), no. 2, 153-160.