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Volumn 218, Issue 1, 2005, Pages 15-35

Multiplicity results for periodic solutions to delay differential equations via critical point theory

Author keywords

Critical point theory; Delay differential equations; Multiple periodic solutions; Pseudo index

Indexed keywords


EID: 27144446664     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jde.2005.08.007     Document Type: Article
Times cited : (71)

References (35)
  • 1
    • 0001232950 scopus 로고
    • On critical point theory for indefinite functionals in the presence of symmetries
    • V. Benci On critical point theory for indefinite functionals in the presence of symmetries Trans. Amer. Math. Soc. 274 1982 533-572
    • (1982) Trans. Amer. Math. Soc. , vol.274 , pp. 533-572
    • Benci, V.1
  • 2
    • 1542437218 scopus 로고
    • Critical point theorems for indefinite functionals
    • V. Benci P.H. Rabinowitz Critical point theorems for indefinite functionals Invent. Math. 53 1979 241-273
    • (1979) Invent. Math. , vol.53 , pp. 241-273
    • Benci, V.1    Rabinowitz, P.H.2
  • 3
    • 84972517829 scopus 로고
    • A further generalization of the Schauder fixed-point theorem
    • F. Browder A further generalization of the Schauder fixed-point theorem Duke Math. J. 32 1965 575-578
    • (1965) Duke Math. J. , vol.32 , pp. 575-578
    • Browder, F.1
  • 6
    • 84966251361 scopus 로고
    • Characteristic multipliers and stability of symmetric periodic solutions of ẋ = g(x(t - 1))
    • S.N. Chow H.O. Walther Characteristic multipliers and stability of symmetric periodic solutions of ẋ = g(x(t - 1)) Trans. Amer. Math. Soc. 307 1988 127-142
    • (1988) Trans. Amer. Math. Soc. , vol.307 , pp. 127-142
    • Chow, S.N.1    Walther, H.O.2
  • 8
    • 84963434618 scopus 로고
    • Existence of periodic solutions of two-dimensional differential delay equations
    • T. Furumochi Existence of periodic solutions of two-dimensional differential delay equations Appl. Anal. 9 1979 279-289
    • (1979) Appl. Anal. , vol.9 , pp. 279-289
    • Furumochi, T.1
  • 9
    • 0001909761 scopus 로고
    • A periodicity theorem for autonomous functional differential equations
    • R.B. Grafton A periodicity theorem for autonomous functional differential equations J. Differential Equations 6 1969 87-109
    • (1969) J. Differential Equations , vol.6 , pp. 87-109
    • Grafton, R.B.1
  • 12
    • 0037431268 scopus 로고    scopus 로고
    • Bifurcations of periodic solutions of delay differential equations
    • M.A. Han Bifurcations of periodic solutions of delay differential equations J. Differential Equations 189 2003 396-411
    • (2003) J. Differential Equations , vol.189 , pp. 396-411
    • Han, M.A.1
  • 13
    • 0003129505 scopus 로고
    • Solutions of ẋ = - g(x(t - 1)) approach Kaplan-Yorke orbits for odd sigmoid g
    • A.V. Herz Solutions of ẋ = - g(x(t - 1)) approach Kaplan-Yorke orbits for odd sigmoid g J. Differential Equations 118 1995 36-53
    • (1995) J. Differential Equations , vol.118 , pp. 36-53
    • Herz, A.V.1
  • 14
    • 0001135605 scopus 로고
    • The existence of periodic solutions of f′(x) = - af(x - 1)[1 + f(x)]
    • G.S. Jones The existence of periodic solutions of f′(x) = - af(x - 1)[1 + f(x)] J. Math. Anal. Appl. 5 1962 435-450
    • (1962) J. Math. Anal. Appl. , vol.5 , pp. 435-450
    • Jones, G.S.1
  • 15
    • 0016128963 scopus 로고
    • Ordinary differential equations which yield periodic solution of delay equations
    • J.L. Kaplan J.A. Yorke Ordinary differential equations which yield periodic solution of delay equations J. Math. Anal. Appl. 48 1974 317-324
    • (1974) J. Math. Anal. Appl. , vol.48 , pp. 317-324
    • Kaplan, J.L.1    Yorke, J.A.2
  • 16
    • 0000874319 scopus 로고
    • On the stability of a periodic solution of a differential delay equation
    • J.L. Kaplan J.A. Yorke On the stability of a periodic solution of a differential delay equation SIAM J. Math. Anal. 6 1975 268-282
    • (1975) SIAM J. Math. Anal. , vol.6 , pp. 268-282
    • Kaplan, J.L.1    Yorke, J.A.2
  • 17
    • 0000120060 scopus 로고
    • On the nonlinear differential delay equation x′(t) = - f(x(t), x(t - 1))
    • J.L. Kaplan J.A. Yorke On the nonlinear differential delay equation x′(t) = - f(x(t), x(t - 1)) J. Differential Equations 23 1977 293-314
    • (1977) J. Differential Equations , vol.23 , pp. 293-314
    • Kaplan, J.L.1    Yorke, J.A.2
  • 18
    • 0031600835 scopus 로고    scopus 로고
    • Multiple periodic solutions of differential delay equations created by asymptotically linear Hamiltonian systems
    • J.B. Li X.Z. He Multiple periodic solutions of differential delay equations created by asymptotically linear Hamiltonian systems Nonlinear Anal. TMA 31 1/2 1998 45-54
    • (1998) Nonlinear Anal. TMA , vol.31 , Issue.1-2 , pp. 45-54
    • Li, J.B.1    He, X.Z.2
  • 19
    • 0042725474 scopus 로고    scopus 로고
    • Proof and generalization of Kaplan-Yorke's conjecture on periodic solution of differential delay equations
    • J.B. Li X.Z. He Proof and generalization of Kaplan-Yorke's conjecture on periodic solution of differential delay equations Sci. China (Ser. A) 42 9 1999 957-964
    • (1999) Sci. China (Ser. A) , vol.42 , Issue.9 , pp. 957-964
    • Li, J.B.1    He, X.Z.2
  • 20
    • 0040036791 scopus 로고    scopus 로고
    • Periodic solutions of some differential delay equations created by Hamiltonian systems
    • J.B. Li X.Z. He Periodic solutions of some differential delay equations created by Hamiltonian systems Bull. Austral. Math. Soc. 60 1999 377-390
    • (1999) Bull. Austral. Math. Soc. , vol.60 , pp. 377-390
    • Li, J.B.1    He, X.Z.2
  • 22
    • 0030102662 scopus 로고    scopus 로고
    • Systems of differential delay equations: Floquet multipliers and discrete Lyapunov functions
    • J. Mallet-Paret G. Sell Systems of differential delay equations: Floquet multipliers and discrete Lyapunov functions J. Differential Equations 125 1996 385-440
    • (1996) J. Differential Equations , vol.125 , pp. 385-440
    • Mallet-Paret, J.1    Sell, G.2
  • 23
    • 0030102885 scopus 로고    scopus 로고
    • The Poincare-Bendixson theorem for monotone cyclic feedback systems with delay
    • J. Mallet-Paret G. Sell The Poincare-Bendixson theorem for monotone cyclic feedback systems with delay J. Differential Equations 125 1996 441-489
    • (1996) J. Differential Equations , vol.125 , pp. 441-489
    • Mallet-Paret, J.1    Sell, G.2
  • 24
    • 0000617020 scopus 로고
    • Periodic solutions of nonlinear functional differential equations
    • J. Mawhin Periodic solutions of nonlinear functional differential equations J. Differential Equations 10 1971 240-261
    • (1971) J. Differential Equations , vol.10 , pp. 240-261
    • Mawhin, J.1
  • 25
    • 0000125085 scopus 로고
    • Equivalence theorems for nonlinear operator equations and coincidence degree theory for some mappings in locally convex topological vector space
    • J. Mawhin Equivalence theorems for nonlinear operator equations and coincidence degree theory for some mappings in locally convex topological vector space J. Differential Equations 12 1972 610-636
    • (1972) J. Differential Equations , vol.12 , pp. 610-636
    • Mawhin, J.1
  • 27
    • 49549172894 scopus 로고
    • Periodic solutions of some nonlinear autonomous functional differential equations, II
    • R.D. Nussbaum Periodic solutions of some nonlinear autonomous functional differential equations, II J. Differential Equations 14 1973 368-394
    • (1973) J. Differential Equations , vol.14 , pp. 368-394
    • Nussbaum, R.D.1
  • 28
    • 0001109202 scopus 로고
    • Periodic solutions of some nonlinear autonomous functional differential equations
    • R.D. Nussbaum Periodic solutions of some nonlinear autonomous functional differential equations Ann. Math. Pura Appl. 10 1974 263-306
    • (1974) Ann. Math. Pura Appl. , vol.10 , pp. 263-306
    • Nussbaum, R.D.1
  • 29
    • 84968466697 scopus 로고
    • A Hopf global bifurcation theorem for retarded functional differential equations
    • R.D. Nussbaum A Hopf global bifurcation theorem for retarded functional differential equations Tran. Amer. Math. Soc. 238 1978 139-163
    • (1978) Tran. Amer. Math. Soc. , vol.238 , pp. 139-163
    • Nussbaum, R.D.1
  • 30
    • 0009838326 scopus 로고
    • Circulant matrices and differential delay equations
    • R.D. Nussbaum Circulant matrices and differential delay equations J. Differential Equations 60 1985 201-217
    • (1985) J. Differential Equations , vol.60 , pp. 201-217
    • Nussbaum, R.D.1
  • 31
    • 84980196930 scopus 로고
    • Periodic solutions of Hamiltonian systems
    • P.H. Rabinowitz Periodic solutions of Hamiltonian systems Comm. Pure Appl. Math. 31 1978 157-184
    • (1978) Comm. Pure Appl. Math. , vol.31 , pp. 157-184
    • Rabinowitz, P.H.1
  • 32
    • 84980174431 scopus 로고
    • On subharmonic solutions of Hamiltonian systems
    • P.H. Rabinowitz On subharmonic solutions of Hamiltonian systems Comm. Pure Appl. Math. 33 1980 609-633
    • (1980) Comm. Pure Appl. Math. , vol.33 , pp. 609-633
    • Rabinowitz, P.H.1
  • 35
    • 0041834529 scopus 로고    scopus 로고
    • Applications of a Zp index theory to periodic solutions for a class of functional differential equations
    • Yuan-Tong Xu Zhi-Ming Guo Applications of a Z p index theory to periodic solutions for a class of functional differential equations J. Math. Anal. Appl. 257 1 2001 189-205
    • (2001) J. Math. Anal. Appl. , vol.257 , Issue.1 , pp. 189-205
    • Xu, Y.-T.1    Guo, Z.-M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.