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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., ().
|
[2] |
J. Campos and M. Tarallo, Almost automorphic linear dynamics by Favard theory, J. Differential Equations, 256 (2014), 1350-1367.
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), 141-159. |
[4] |
H. Dym, Linear Algebra in Action, Graduate Studies in Mathematics, Vol. 78, AMS, Prividence, 2007. |
[5] |
J. Favard, Sur les equations différentielles linéairesà coefficients presque-périodiques, Acta Math. , 51 (1928), 31-81.
doi: 10.1007/BF02545660. |
[6] |
J. K. Hale, Ordinary Differential Equations, Pure and Applied Mathematics, Vol. XXI, Wiley-Interscience, New York, 1969. |
[7] |
J. C. Lillo, Approximate similarity and almost periodic matrices, Proc. Amer. Math. Soc., 12 (1961), 400-407. |
[8] |
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. |
[9] |
K. J. Palmer, On bounded solutions of almost periodic linear differential systems, J. Math. Anal. Appl., 103 (1984), 16-25.
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), 429-458.
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), 478-496.
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), 497-522.
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), 320-358.
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), 2301-2313.
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), 291-304.
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., ().
|
[2] |
J. Campos and M. Tarallo, Almost automorphic linear dynamics by Favard theory, J. Differential Equations, 256 (2014), 1350-1367.
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), 141-159. |
[4] |
H. Dym, Linear Algebra in Action, Graduate Studies in Mathematics, Vol. 78, AMS, Prividence, 2007. |
[5] |
J. Favard, Sur les equations différentielles linéairesà coefficients presque-périodiques, Acta Math. , 51 (1928), 31-81.
doi: 10.1007/BF02545660. |
[6] |
J. K. Hale, Ordinary Differential Equations, Pure and Applied Mathematics, Vol. XXI, Wiley-Interscience, New York, 1969. |
[7] |
J. C. Lillo, Approximate similarity and almost periodic matrices, Proc. Amer. Math. Soc., 12 (1961), 400-407. |
[8] |
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. |
[9] |
K. J. Palmer, On bounded solutions of almost periodic linear differential systems, J. Math. Anal. Appl., 103 (1984), 16-25.
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), 429-458.
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), 478-496.
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), 497-522.
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), 320-358.
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), 2301-2313.
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), 291-304.
doi: 10.1007/s10884-013-9309-2. |
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