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Recurrent equations with sign and Fredholm alternative
1. | Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada |
2. | Departamento de Matemática Aplicada, Universidad de Valladolid, Paseo del Cauce 59, 47011 Valladolid |
3. | Università di Milano, via Saldini 50, 20133 Milano, Italy |
References:
[1] |
J. Campos, R. Obaya and M. Tarallo, Favard theory for the adjoint equation and Fredholm Alternative,, preprint., (). Google Scholar |
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J. Campos and M. Tarallo, Almost automorphic linear dynamics by Favard theory,, J. Differential Equations, 256 (2014), 1350.
doi: 10.1016/j.jde.2013.10.018. |
[3] |
P. Cieutat and A. Haraux, Exponential decay and existence of almost periodic solutions for some linear forced differential equations,, Port. Math., 59 (2002), 141.
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H. Dym, Linear Algebra in Action,, Graduate Studies in Mathematics, (2007). Google Scholar |
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J. Favard, Sur les equations différentielles linéairesà coefficients presque-périodiques,, Acta Math. , 51 (1928), 31.
doi: 10.1007/BF02545660. |
[6] |
J. K. Hale, Ordinary Differential Equations,, Pure and Applied Mathematics, (1969).
|
[7] |
J. C. Lillo, Approximate similarity and almost periodic matrices,, Proc. Amer. Math. Soc., 12 (1961), 400.
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[8] |
R. Ortega and M. Tarallo, Almost periodic equations and conditions of Ambrosetti-Prodi type,, Math. Proc. Camb. Phil. Soc., 135 (2003), 239.
doi: 10.1017/S0305004103006662. |
[9] |
K. J. Palmer, On bounded solutions of almost periodic linear differential systems,, J. Math. Anal. Appl., 103 (1984), 16.
doi: 10.1016/0022-247X(84)90152-5. |
[10] |
R. J. Sacker and G. R. Sell, Existence of dichotomies and invariant splittings for linear differential systems. I,, J. Differential Equations, 15 (1974), 429.
doi: 10.1016/0022-0396(74)90067-9. |
[11] |
R. J. Sacker and G. R. Sell, Existence of dichotomies and invariant splittings for linear differential systems. II,, J. Differential Equations, 22 (1976), 478.
doi: 10.1016/0022-0396(76)90042-5. |
[12] |
R. J. Sacker and G. R. Sell, Existence of dichotomies and invariant splittings for linear differential systems. III,, J. Differential Equations, 22 (1976), 497.
doi: 10.1016/0022-0396(76)90043-7. |
[13] |
R. J. Sacker and G. R. Sell, A spectral theory for linear differential systems,, J. Differential Equations, 27 (1978), 320.
doi: 10.1016/0022-0396(78)90057-8. |
[14] |
M. Tarallo, Fredholm's alternative for a class of almost periodic linear systems,, Discrete Contin. Dyn. Syst., 32 (2012), 2301.
doi: 10.3934/dcds.2012.32.2301. |
[15] |
M. Tarallo, The Favard separation condition as a purely dimensional fact,, J. Dyn. Diff. Equations, 25 (2013), 291.
doi: 10.1007/s10884-013-9309-2. |
show all references
References:
[1] |
J. Campos, R. Obaya and M. Tarallo, Favard theory for the adjoint equation and Fredholm Alternative,, preprint., (). Google Scholar |
[2] |
J. Campos and M. Tarallo, Almost automorphic linear dynamics by Favard theory,, J. Differential Equations, 256 (2014), 1350.
doi: 10.1016/j.jde.2013.10.018. |
[3] |
P. Cieutat and A. Haraux, Exponential decay and existence of almost periodic solutions for some linear forced differential equations,, Port. Math., 59 (2002), 141.
|
[4] |
H. Dym, Linear Algebra in Action,, Graduate Studies in Mathematics, (2007). Google Scholar |
[5] |
J. Favard, Sur les equations différentielles linéairesà coefficients presque-périodiques,, Acta Math. , 51 (1928), 31.
doi: 10.1007/BF02545660. |
[6] |
J. K. Hale, Ordinary Differential Equations,, Pure and Applied Mathematics, (1969).
|
[7] |
J. C. Lillo, Approximate similarity and almost periodic matrices,, Proc. Amer. Math. Soc., 12 (1961), 400.
|
[8] |
R. Ortega and M. Tarallo, Almost periodic equations and conditions of Ambrosetti-Prodi type,, Math. Proc. Camb. Phil. Soc., 135 (2003), 239.
doi: 10.1017/S0305004103006662. |
[9] |
K. J. Palmer, On bounded solutions of almost periodic linear differential systems,, J. Math. Anal. Appl., 103 (1984), 16.
doi: 10.1016/0022-247X(84)90152-5. |
[10] |
R. J. Sacker and G. R. Sell, Existence of dichotomies and invariant splittings for linear differential systems. I,, J. Differential Equations, 15 (1974), 429.
doi: 10.1016/0022-0396(74)90067-9. |
[11] |
R. J. Sacker and G. R. Sell, Existence of dichotomies and invariant splittings for linear differential systems. II,, J. Differential Equations, 22 (1976), 478.
doi: 10.1016/0022-0396(76)90042-5. |
[12] |
R. J. Sacker and G. R. Sell, Existence of dichotomies and invariant splittings for linear differential systems. III,, J. Differential Equations, 22 (1976), 497.
doi: 10.1016/0022-0396(76)90043-7. |
[13] |
R. J. Sacker and G. R. Sell, A spectral theory for linear differential systems,, J. Differential Equations, 27 (1978), 320.
doi: 10.1016/0022-0396(78)90057-8. |
[14] |
M. Tarallo, Fredholm's alternative for a class of almost periodic linear systems,, Discrete Contin. Dyn. Syst., 32 (2012), 2301.
doi: 10.3934/dcds.2012.32.2301. |
[15] |
M. Tarallo, The Favard separation condition as a purely dimensional fact,, J. Dyn. Diff. Equations, 25 (2013), 291.
doi: 10.1007/s10884-013-9309-2. |
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