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Multibump solutions of nonlinear Schrödinger equations with steep potential well and indefinite potential
On general properties of retarded functional differential equations on manifolds
1. | Dipartimento di Sistemi e Informatica, Università degli Studi di Firenze, Via S. Marta 3, I-50139 Firenze, Italy, Italy, Italy |
2. | Dipartimento di Ingegneria Industriale e Scienze Matematiche, Università Politecnica delle Marche, Via Brecce Bianche, I-60131 Ancona, Italy |
References:
[1] |
P. Benevieri, A. Calamai, M. Furi and M. P. Pera, Retarded functional differential equations on manifolds and applications to motion problems for forced constrained systems, Adv. Nonlinear Stud., 9 (2009), 199-214. |
[2] |
P. Benevieri, A. Calamai, M. Furi and M. P. Pera, A continuation result for forced oscillations of constrained motion problems with infinite delay,, to appear in Adv. Nonlinear Stud., ().
|
[3] |
P. Benevieri, A. Calamai, M. Furi and M. P. Pera, On the existence of forced oscillations for the spherical pendulum acted on by a retarded periodic force, J. Dyn. Diff. Equat., 23 (2011), 541-549.
doi: 10.1007/s10884-010-9201-2. |
[4] |
G. Bouligand, "Introduction à la Géométrie Infinitésimale Directe,'' Gauthier-Villard, Paris, 1932. |
[5] |
N. Dunford and J. T. Schwartz, "Linear Operators,'' Wiley & Sons, Inc., New York, 1957. |
[6] |
R. Gaines and J. Mawhin, "Coincidence Degree and Nonlinear Differential Equations,'' Lecture Notes in Math., Springer Verlag, Berlin, 568, 1977. |
[7] |
V. Guillemin and A. Pollack, "Differential Topology,'' Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1974. |
[8] |
J. K. Hale and J. Kato, Phase space for retarded equations with infinite delay, Funkc. Ekvac., 21 (1978), 11-41. |
[9] |
J. K. Hale and S. M. Verduyn Lunel, "Introduction to Functional Differential Equations,'' Springer Verlag, New York, 1993. |
[10] |
Y. Hino, S. Murakami and T. Naito, "Functional-Differential Equations with Infinite Delay,'' Lecture Notes in Math., Springer Verlag, Berlin, 1473, 1991. |
[11] |
M. W. Hirsch, "Differential Topology,'' Graduate Texts in Math., Springer Verlag, Berlin, 33, 1976. |
[12] |
J. Mallet-Paret, R. D. Nussbaum and P. Paraskevopoulos, Periodic solutions for functional-differential equations with multiple state-dependent time lags, Topol. Methods Nonlinear Anal., 3 (1994), 101-162. |
[13] |
J. M. Milnor, "Topology from the Differentiable Viewpoint,'' Univ. Press of Virginia, Charlottesville, 1965. |
[14] |
J. R. Munkres, "Elementary Differential Topology,'' Princeton University Press, Princeton, New Jersey, 1966. |
[15] |
R. D. Nussbaum, Periodic solutions of some nonlinear autonomous functional differential equations, Ann. Mat. Pura Appl., 101 (1974), 263-306.
doi: 10.1007/BF02417109. |
[16] |
R. D. Nussbaum, The fixed point index and fixed point theorems, in "Topological methods for ordinary differential equations'' (Montecatini Terme, 1991), Lecture Notes in Math., Springer Verlag, Berlin, 1537 (1993), 143-205. |
[17] |
W. M. Oliva, Functional differential equations on compact manifolds and an approximation theorem, J. Differential Equations, 5 (1969), 483-496. |
[18] |
W. M. Oliva, Functional differential equations-generic theory, in "Dynamical Systems'' (Proc. Internat. Sympos., Brown Univ., Providence, R. I., 1974), Academic Press, New York, (1976), 195-209. |
[19] |
W. M. Oliva and C. Rocha, Reducible volterra and levin-nohel retarded equations with infinite delay, J. Dyn. Diff. Equat., 22 (2010), 509-532.
doi: 10.1007/s10884-010-9177-y. |
show all references
References:
[1] |
P. Benevieri, A. Calamai, M. Furi and M. P. Pera, Retarded functional differential equations on manifolds and applications to motion problems for forced constrained systems, Adv. Nonlinear Stud., 9 (2009), 199-214. |
[2] |
P. Benevieri, A. Calamai, M. Furi and M. P. Pera, A continuation result for forced oscillations of constrained motion problems with infinite delay,, to appear in Adv. Nonlinear Stud., ().
|
[3] |
P. Benevieri, A. Calamai, M. Furi and M. P. Pera, On the existence of forced oscillations for the spherical pendulum acted on by a retarded periodic force, J. Dyn. Diff. Equat., 23 (2011), 541-549.
doi: 10.1007/s10884-010-9201-2. |
[4] |
G. Bouligand, "Introduction à la Géométrie Infinitésimale Directe,'' Gauthier-Villard, Paris, 1932. |
[5] |
N. Dunford and J. T. Schwartz, "Linear Operators,'' Wiley & Sons, Inc., New York, 1957. |
[6] |
R. Gaines and J. Mawhin, "Coincidence Degree and Nonlinear Differential Equations,'' Lecture Notes in Math., Springer Verlag, Berlin, 568, 1977. |
[7] |
V. Guillemin and A. Pollack, "Differential Topology,'' Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1974. |
[8] |
J. K. Hale and J. Kato, Phase space for retarded equations with infinite delay, Funkc. Ekvac., 21 (1978), 11-41. |
[9] |
J. K. Hale and S. M. Verduyn Lunel, "Introduction to Functional Differential Equations,'' Springer Verlag, New York, 1993. |
[10] |
Y. Hino, S. Murakami and T. Naito, "Functional-Differential Equations with Infinite Delay,'' Lecture Notes in Math., Springer Verlag, Berlin, 1473, 1991. |
[11] |
M. W. Hirsch, "Differential Topology,'' Graduate Texts in Math., Springer Verlag, Berlin, 33, 1976. |
[12] |
J. Mallet-Paret, R. D. Nussbaum and P. Paraskevopoulos, Periodic solutions for functional-differential equations with multiple state-dependent time lags, Topol. Methods Nonlinear Anal., 3 (1994), 101-162. |
[13] |
J. M. Milnor, "Topology from the Differentiable Viewpoint,'' Univ. Press of Virginia, Charlottesville, 1965. |
[14] |
J. R. Munkres, "Elementary Differential Topology,'' Princeton University Press, Princeton, New Jersey, 1966. |
[15] |
R. D. Nussbaum, Periodic solutions of some nonlinear autonomous functional differential equations, Ann. Mat. Pura Appl., 101 (1974), 263-306.
doi: 10.1007/BF02417109. |
[16] |
R. D. Nussbaum, The fixed point index and fixed point theorems, in "Topological methods for ordinary differential equations'' (Montecatini Terme, 1991), Lecture Notes in Math., Springer Verlag, Berlin, 1537 (1993), 143-205. |
[17] |
W. M. Oliva, Functional differential equations on compact manifolds and an approximation theorem, J. Differential Equations, 5 (1969), 483-496. |
[18] |
W. M. Oliva, Functional differential equations-generic theory, in "Dynamical Systems'' (Proc. Internat. Sympos., Brown Univ., Providence, R. I., 1974), Academic Press, New York, (1976), 195-209. |
[19] |
W. M. Oliva and C. Rocha, Reducible volterra and levin-nohel retarded equations with infinite delay, J. Dyn. Diff. Equat., 22 (2010), 509-532.
doi: 10.1007/s10884-010-9177-y. |
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