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An infinite dimensional bifurcation problem with application to a class of functional differential equations of neutral type
| 1. | Université de Metz, Mathématiques, LMAM, Ile du Saulcy, 57045 Metz, France |
| 2. | Voronezh State University, Department of Mathematics, Universitetskaya pl. 1, 394006 Voronezh, Russian Federation |
| 3. | Dipartimento di Ingegneria dell' Informazione, Università di Siena, Via Roma 56, 53100, Siena |
References:
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J. Cronin, "Differential Equations: Introduction and Qualitative Theory," Pure and Applied Mathematics, A Series of Monographs and Textbooks, 54, Marcel Dekker, Inc. New York and Basel, 1980. |
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I. C. Gohberg, S. Golberg and M. A. Kaashoek, "Classes of Linear Operators I," Operator Theory: Advances and Applications, 49, Birkhäuser Verlag, Basel, 1990. |
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I. C. Gohberg and M. G. Krein, The basic proposition on defect numbers, root numbers and indexes of linear operators, Amer. Math. Soc. Transl., 13 (1960), 185-264. |
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M. I. Kamenskii, O. Makarenkov and P. Nistri, An alternative approach to study bifurcation from a limit cycle in periodically perturbed autonomous systems, J. Dyn. Diff. Equat., 23 (2011), 425-435.
doi: 10.1007/s10884-011-9207-4. |
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S. G. Krantz and H. R. Parks, "The Implicit Function Theorem: History, Theory and Applications," Birkhäuser, Boston, 2003. |
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W. S. Loud, Periodic solutions of a perturbed autonomous system, Ann. Math., 70 (1959), 490-529. |
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I. G. Malkin, "Some Problems of the Theory of Nonlinear Oscillations," (Russian) Gosudarstv. Isdat. Techn. Teor. Lit., Moscow, 1956. |
show all references
References:
| [1] |
J. Cronin, "Differential Equations: Introduction and Qualitative Theory," Pure and Applied Mathematics, A Series of Monographs and Textbooks, 54, Marcel Dekker, Inc. New York and Basel, 1980. |
| [2] |
I. C. Gohberg, S. Golberg and M. A. Kaashoek, "Classes of Linear Operators I," Operator Theory: Advances and Applications, 49, Birkhäuser Verlag, Basel, 1990. |
| [3] |
I. C. Gohberg and M. G. Krein, The basic proposition on defect numbers, root numbers and indexes of linear operators, Amer. Math. Soc. Transl., 13 (1960), 185-264. |
| [4] |
M. I. Kamenskii, O. Makarenkov and P. Nistri, An alternative approach to study bifurcation from a limit cycle in periodically perturbed autonomous systems, J. Dyn. Diff. Equat., 23 (2011), 425-435.
doi: 10.1007/s10884-011-9207-4. |
| [5] |
S. G. Krantz and H. R. Parks, "The Implicit Function Theorem: History, Theory and Applications," Birkhäuser, Boston, 2003. |
| [6] |
W. S. Loud, Periodic solutions of a perturbed autonomous system, Ann. Math., 70 (1959), 490-529. |
| [7] |
I. G. Malkin, "Some Problems of the Theory of Nonlinear Oscillations," (Russian) Gosudarstv. Isdat. Techn. Teor. Lit., Moscow, 1956. |
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