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Fredholm's alternative for a class of almost periodic linear systems
| 1. | Università degli Studi di Milano, Via C. Saldini 50, Milano, I–20133, Italy |
References:
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W. A. Coppel, "Dichotomies in Stability Theory," Lecture Notes in Mathematics, Vol. 629, Springer-Verlag, Berlin-New York, 1978. |
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J. Favard, Sur les équations différentielles linéaires à coefficients presque-périodiques, (French) [On the linear differential equations with almost peridoic coefficients], Acta Math., 51 (1928), 31-81.
doi: 10.1007/BF02545660. |
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J. Favard, Sur certains systèmes différentiels scalaires linéaires et homogénes à coefficients presque-périodiques, (French) [On some scalar linear homogeneous differential systems with almost periodic coefficients], Ann. Mat. Pura Appl. (4), 61 (1963), 297-316. |
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A. M. Fink, "Almost Periodic Differential Equations," Lecture Notes in Mathematics, Vol. 377, Springer-Verlag, Berlin-New York, 1974. |
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J. K. Hale, "Ordinary Differential Equations," Pure and Applied Mathematics, Vol. XXI, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1969. |
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R. A. Johnson, A linear, almost periodic equation with an almost automorphic solution, Proc. Amer. Math. Soc., 82 (1981), 199-205.
doi: 10.1090/S0002-9939-1981-0609651-0. |
| [7] |
R. Ortega and M. Tarallo, Almost periodic equations and conditions of Ambrosetti-Prodi type, Math. Proc. Camb. Phil. Soc., 135 (2003), 239-254.
doi: 10.1017/S0305004103006662. |
| [8] |
R. Ortega and M. Tarallo, Almost periodic linear differential equations with non-separated solutions, J. Funct. Analysis, 237 (2006), 402-426.
doi: 10.1016/j.jfa.2006.03.027. |
| [9] |
K. J. Palmer, Exponential dichotomies and transversal homoclinic points, J. Differential Equations, 55 (1984), 225-256.
doi: 10.1016/0022-0396(84)90082-2. |
| [10] |
K. J. Palmer, Exponential dichotomies and Fredholm operators, Proc. Amer. Mat. Soc., 104 (1988), 149-156.
doi: 10.1090/S0002-9939-1988-0958058-1. |
| [11] |
H. M. Rodrigues and M. Silveira, On the relationship between exponential dichotomies and Fredholm alternative, J. Differential Equations, 73 (1988), 78-81.
doi: 10.1016/0022-0396(88)90118-0. |
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M. Tarallo, Module containment property for linear equations, J. Differential Equations, 224 (2008), 52-60.
doi: 10.1016/j.jde.2007.10.006. |
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V. V. Žhikov and B. M. Levitan, Favard theory, Uspehi Mat. Nauk, 32 (1977), 123-171, 263. |
show all references
References:
| [1] |
W. A. Coppel, "Dichotomies in Stability Theory," Lecture Notes in Mathematics, Vol. 629, Springer-Verlag, Berlin-New York, 1978. |
| [2] |
J. Favard, Sur les équations différentielles linéaires à coefficients presque-périodiques, (French) [On the linear differential equations with almost peridoic coefficients], Acta Math., 51 (1928), 31-81.
doi: 10.1007/BF02545660. |
| [3] |
J. Favard, Sur certains systèmes différentiels scalaires linéaires et homogénes à coefficients presque-périodiques, (French) [On some scalar linear homogeneous differential systems with almost periodic coefficients], Ann. Mat. Pura Appl. (4), 61 (1963), 297-316. |
| [4] |
A. M. Fink, "Almost Periodic Differential Equations," Lecture Notes in Mathematics, Vol. 377, Springer-Verlag, Berlin-New York, 1974. |
| [5] |
J. K. Hale, "Ordinary Differential Equations," Pure and Applied Mathematics, Vol. XXI, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1969. |
| [6] |
R. A. Johnson, A linear, almost periodic equation with an almost automorphic solution, Proc. Amer. Math. Soc., 82 (1981), 199-205.
doi: 10.1090/S0002-9939-1981-0609651-0. |
| [7] |
R. Ortega and M. Tarallo, Almost periodic equations and conditions of Ambrosetti-Prodi type, Math. Proc. Camb. Phil. Soc., 135 (2003), 239-254.
doi: 10.1017/S0305004103006662. |
| [8] |
R. Ortega and M. Tarallo, Almost periodic linear differential equations with non-separated solutions, J. Funct. Analysis, 237 (2006), 402-426.
doi: 10.1016/j.jfa.2006.03.027. |
| [9] |
K. J. Palmer, Exponential dichotomies and transversal homoclinic points, J. Differential Equations, 55 (1984), 225-256.
doi: 10.1016/0022-0396(84)90082-2. |
| [10] |
K. J. Palmer, Exponential dichotomies and Fredholm operators, Proc. Amer. Mat. Soc., 104 (1988), 149-156.
doi: 10.1090/S0002-9939-1988-0958058-1. |
| [11] |
H. M. Rodrigues and M. Silveira, On the relationship between exponential dichotomies and Fredholm alternative, J. Differential Equations, 73 (1988), 78-81.
doi: 10.1016/0022-0396(88)90118-0. |
| [12] |
M. Tarallo, Module containment property for linear equations, J. Differential Equations, 224 (2008), 52-60.
doi: 10.1016/j.jde.2007.10.006. |
| [13] |
V. V. Žhikov and B. M. Levitan, Favard theory, Uspehi Mat. Nauk, 32 (1977), 123-171, 263. |
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