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

$C^{\alpha}$-Hölder classical solutions for non-autonomous neutral differential equations

Abstract Related Papers Cited by
  • In this paper we discuss the existence of α-Hölder classical solutions for non-autonomous abstract partial neutral functional differential equations. An application is considered.
    Mathematics Subject Classification: Primary: 35R10, 34K40; Secondary: 34K30.

    Citation:

    \begin{equation} \\ \end{equation}
  • [1]

    M. Adimy and K. Ezzinbi, A class of linear partial neutral functional-differential equations with nondense domain, J. Diff. Eqns., 147 (1998), 285-332.doi: doi:10.1006/jdeq.1998.3446.

    [2]

    K. Balachandran, G. Shija and J. Kim, Existence of solutions of nonlinear abstract neutral integrodifferential equations, Comput. Math. Appl., 48 (2004), 1403-1414.doi: doi:10.1016/j.camwa.2004.08.002.

    [3]

    K. Balachandran and R. Sakthivel, Existence of solutions of neutral functional integrodifferential equation in Banach spaces, Proc. Indian Acad. Sci. Math. Sci., 109 (1999), 325-332.doi: doi:10.1007/BF02843536.

    [4]

    M. Benchohra and S. Ntouyas, Nonlocal Cauchy problems for neutral functional differential and integrodifferential inclusions in Banach spaces, J. Math. Anal. Appl., 258 (2001), 573-590.doi: doi:10.1006/jmaa.2000.7394.

    [5]

    M. Benchohra, J. Henderson and S. Ntouyas, Existence results for impulsive multivalued semilinear neutral functional differential inclusions in Banach spaces, J. Math. Anal. Appl., 263 (2001), 763-780.doi: doi:10.1006/jmaa.2001.7663.

    [6]

    J. P. Dauer and K. Balachandran, Existence of solutions of nonlinear neutral integrodifferential equations in Banach spaces, J. Math. Anal. Appl., 251 (2000), 93-105.doi: doi:10.1006/jmaa.2000.7022.

    [7]

    P. Cannarsa and D. Sforza, Global solutions of abstract semilinear parabolic equations with memory terms, NoDEA Nonlinear Differential Equations. Appl., 10 (2003), 399-430.

    [8]

    Ph. Clément and J. A. Nohel, Asymptotic behavior of solutions of nonlinear Volterra equations with completely positive kernels, SIAM J. Math. Anal., 12 (1981), 514-535.doi: doi:10.1137/0512045.

    [9]

    Ph. Clément and J. Prüss, Global existence for a semilinear parabolic Volterra equation, Math. Z., 209 (1992), 17-26.doi: doi:10.1007/BF02570816.

    [10]

    R. Datko, Linear autonomous neutral differential equations in a Banach space, J. Diff. Equations, 25 (1977), 258-274.doi: doi:10.1016/0022-0396(77)90204-2.

    [11]

    H. Fang and J. Li, On the existence of periodic solutions of a neutral delay model of single-species population growth, J. Math. Anal. Appl., 259 (2001), 8-17.doi: doi:10.1006/jmaa.2000.7340.

    [12]

    X. Fu and X. Liu, Existence of periodic solutions for abstract neutral non-autonomous equations with infinite delay, J. Math. Anal. Appl., 325 (2007), 249-267.doi: doi:10.1016/j.jmaa.2006.01.048.

    [13]

    H. I. Freedman and Y. Kuang, Some global qualitative analyses of a single species neutral delay differential population model, "Second Geoffrey J. Butler Memorial Conference in Differential Equations and Mathematical Biology" (Edmonton, AB, 1992), Rocky Mountain J. Math., 25 (1995), 201-215.doi: doi:10.1216/rmjm/1181072278.

    [14]

    M. E. Gurtin and A. C. Pipkin, A general theory of heat conduction with finite wave speed, Arch. Rat. Mech. Anal., 31 (1968), 113-126.doi: doi:10.1007/BF00281373.

    [15]

    J. Hale and S. M. Verduyn Lunel, "Introduction to Functional-Differential Equations," Applied Mathematical Sciences, 99, Springer-Verlag, New York, 1993.

    [16]

    J. K. Hale, Partial neutral functional-differential equations, Rev. Roumaine Math Pures Appl, 39 (1994), 339-344.

    [17]

    H. Henriquez, Periodic solutions of abstract neutral functional differential equations with infinite delay, Acta Math. Hungar., 121 (2008), 203-227.doi: doi:10.1007/s10474-008-7009-x.

    [18]

    E. Hernández and D. O'Regan, Existence results for abstract partial neutral differential equations, Proc. Amer. Math. Soc., 137 (2009), 3309-3318.doi: doi:10.1090/S0002-9939-09-09934-1.

    [19]

    E. Hernández and H. Henríquez, Existence results for partial neutral functional differential equation with unbounded delay, J. Math. Anal. Appl., 221 (1998), 452-475.doi: doi:10.1006/jmaa.1997.5875.

    [20]

    E. Hernández, Existence results for partial neutral integrodifferential equations with unbounded delay, J. Math. Anal. Appl., 292 (2004), 194-210.doi: doi:10.1016/j.jmaa.2003.11.052.

    [21]

    E. Hernández and H. Henríquez, Existence of periodic solution of partial neutral functional differential equation with unbounded delay, J. Math. Anal. Appl., 221 (1998), 499-522.doi: doi:10.1006/jmaa.1997.5899.

    [22]

    Y. Kuang, Qualitative analysis of one- or two-species neutral delay population models, SIAM J. Math. Anal., 23 (1992), 181-200.doi: doi:10.1137/0523009.

    [23]

    Q. Li, J. Cao and S. Wan, Positive periodic solution for a neutral delay model in population, J. Biomath., 13 (1998), 435-438.

    [24]

    A. Lunardi, On the linear heat equation with fading memory, SIAM J. Math. Anal., 21 (1990), 1213-1224.doi: doi:10.1137/0521066.

    [25]

    A. Lunardi., "Analytic Semigroups and Optimal Regularity in Parabolic Problems," PNLDE, 16, Birkhäuser Verlag, Basel, 1995.

    [26]

    J. W. Nunziato, On heat conduction in materials with memory, Quart. Appl. Math., 29 (1971), 187-204.

    [27]

    A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations," Applied Mathematical Sciences, 44, Springer-Verlag, New York-Berlin, 1983.

    [28]

    J. Wu and Xia Huaxing, Self-sustained oscillations in a ring array of coupled lossless transmission lines, J. Differential Equations, 124 (1996), 247-278.doi: doi:10.1006/jdeq.1996.0009.

  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(95) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return