\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Recurrent equations with sign and Fredholm alternative

Abstract / Introduction Related Papers Cited by
  • We prove that a Fredholm--type Alternative holds for recurrent equations with sign, extending a previous result by Cieutat and Haraux in [3]. Moreover, we show that this can be seen a particular case of [1] and we provide a solution to an interesting question raised by Hale in [6]. Finally we characterize the existence of exponential dichotomies also in the nonrecurrent case.
    Mathematics Subject Classification: Primary: 34C27; Secondary: 34B05, 34A30.

    Citation:

    \begin{equation} \\ \end{equation}
  • [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.

  • 加载中
SHARE

Article Metrics

HTML views(1027) PDF downloads(152) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return