Existence and uniqueness of anti-periodic solutions for a class of nonlinear n-th order functional differential equations

• Autorzy: Liu L. , Li Y.
• Języki publikacji: EN

Słowa kluczowe

EN

anti-periodic solution; coincidence degree; nonlinear n-th-order equation; delay

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2011
• Tom: Vol. 31, no. 1
• Strony: 61--74
• Opis fizyczny: Bibliogr. 24 poz.

Twórcy

autor

Liu L.

autor

Li Y.

• Yunnan University Department of Mathematics Kunming, Yunnan 650091, P.R. China,

Bibliografia

• [1] Q.Y. Fan, W.T.Wang, X.J. Yi, Anti-periodic solutions for a class of nonlinear nth-order differential equations with delays, J. Comput. Appl. Math. 230 (2009), 762-769.
• [2] S. Lu, Z. Gui, On the existence of periodic solutions to p-Laplacian Rayleigh differential equation with a delay, J. Math. Anal. Appl. 325 (2007), 685-702.
• [3] M. Zong, H. Liang, Periodic solutions for Rayleigh type p-Laplacian equation with deviating arguments, Appl. Math. Lett. 206 (2007), 43-47.
• [4] F. Zhang, Y. Li, Existence and uniqueness of periodic solutions for a kind of doffing type p-Laplacian equation, Nonlinear Anal.: RWA 9 (2008) 3, 985-989.
• [5] H. Gao, B.W. Liu, Existence and uniqueness of periodic solutions for forced Rayleigh-type equations, Appl. Math. Comp. 211 (2009), 148-154.
• [6] Y. Wang, L. Zhang, Existence of asymptotically stable periodic solutions of a Rayleigh type equation, Nonlinear Analysis 71 (2009), 1728-1735.
• [7] H. Chen, K. Li, D. Li, On the existence of exactly one and two periodic solutions of Liénard equation, Acta Math. Sinica 47 (2004) 3, 417-424 [in Chinese].
• [8] T. Chen, W. Liu, J. Zhang, M. Zhang, The existence of anti-periodic solutions for Liénard equations, J. Math. Study 40 (2007), 187-195 [in Chinese].
• [9] S.P. Lu, Existence of periodic solutions to a p-Laplacian Lienard differential equation with a deviating argument, Nonlinear Analysis: Theory, Methods & Applications 68 (2008), 1453-1461.
• [10] H. Okochi, On the existence of anti-periodic solutions to nonlinear parabolic equations in noncylindrical domains, Nonlinear Anal. 14 (1990), 771-783.
• [11] S. Aizicovici, N.H. Pavel, Anti-periodic solutions to a class of nonlinear differential equations in Hilbert space, J. Funct. Anal. 99 (1991), 387-408.
• [12] A.R. Aftabizadeh, S. Aizicovici, N.H. Pavel, On a class of second-order anti-periodic boundary value problems, J. Math. Anal. Appl. 171 (1992), 301-320.
• [13] A.R. Aftabizadeh, N.H. Pavel, Y.K. Huang, Anti-periodic oscillations of some second-order differential equations and optimal control problems, J. Comput. Appl. Math. 52 (1994), 3-21.
• [14] Y.Q. Chen, Anti-periodic solutions for semilinear evolution equations, J. Math. Anal. Appl. 315 (2006), 337-348.
• [15] W. Ding, Y.P. Xing, M.A. Han, Anti-periodic boundary value problems for first order impulsive functional differential equations, Appl. Math. Comput. 186 (2007), 45-53.
• [16] Y.Q. Chen, J.J. Nieto, D. O'Regan, Anti-periodic solutions for fully nonlinear first-order differential equations, Math. Comput. Modelling 46 (2007), 1183-1190.
• [17] C.X. Ou, Anti-periodic solutions for high-order Hopfield neural networks, Comput. Math. Appl. 56 (2008), 1838-1844.
• [18] Z.H. Liu, Anti-periodic solutions to nonlinear evolution equations, J. Funct. Anal. 258 (2010), 2026-2033.
• [19] F.J. Delvos, L. Knoche, Lacunary interpolation by antiperiodic trigonometric polynomials, BIT 39 (1999), 439-450.
• [20] J.Y. Du, H.L. Han, G.X. Jin, On trigonometric and paratrigonometric Hermite interpolation, J. Approx. Theory 131 (2004), 74-99.
• [21] H.L. Chen, Antiperiodic wavelets, J. Comput. Math. 14 (1996), 32-39. 74 Ling Liu, Yongkun Li
• [22] D. O'Regan, Y.J. Chao, Y.Q. Chen, Topological Degree Theory and Application, Taylor and Francis Group, Boca Raton, London, New York, 2006.
• [23] J. Mawhin, An extension of a theorem of A.C. Lazer on forced nonlinear oscillations, J. Math. Anal. Appl. 40 (1972), 20-29.
• [24] J. Mawhin, M. Willem, Critical Point Theory and Hamiltonian Systems, Appl. Math. Sci, vol. 74, Spring-Verlag, New York, 1989.