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$C^{\alpha}$-Hölder classical solutions for non-autonomous neutral differential equations
1. | Departamento de Física e Matemática, Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto. Universidade de São Paulo, Ribeirão Preto, SP, Cp 14040-901, Brazil |
2. | Department of Mathematics, National University of Ireland, Galway |
References:
[1] |
M. Adimy and K. Ezzinbi, A class of linear partial neutral functional-differential equations with nondense domain,, J. Diff. Eqns., 147 (1998), 285.
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.
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.
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.
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.
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.
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.
|
[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.
doi: doi:10.1137/0512045. |
[9] |
Ph. Clément and J. Prüss, Global existence for a semilinear parabolic Volterra equation,, Math. Z., 209 (1992), 17.
doi: doi:10.1007/BF02570816. |
[10] |
R. Datko, Linear autonomous neutral differential equations in a Banach space,, J. Diff. Equations, 25 (1977), 258.
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.
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.
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,, Rocky Mountain J. Math., 25 (1995), 201.
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.
doi: doi:10.1007/BF00281373. |
[15] |
J. Hale and S. M. Verduyn Lunel, "Introduction to Functional-Differential Equations,", Applied Mathematical Sciences, 99 (1993).
|
[16] |
J. K. Hale, Partial neutral functional-differential equations,, Rev. Roumaine Math Pures Appl, 39 (1994), 339.
|
[17] |
H. Henriquez, Periodic solutions of abstract neutral functional differential equations with infinite delay,, Acta Math. Hungar., 121 (2008), 203.
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.
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.
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.
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.
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.
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.
|
[24] |
A. Lunardi, On the linear heat equation with fading memory,, SIAM J. Math. Anal., 21 (1990), 1213.
doi: doi:10.1137/0521066. |
[25] |
A. Lunardi., "Analytic Semigroups and Optimal Regularity in Parabolic Problems,", PNLDE, 16 (1995).
|
[26] |
J. W. Nunziato, On heat conduction in materials with memory,, Quart. Appl. Math., 29 (1971), 187.
|
[27] |
A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations,", Applied Mathematical Sciences, 44 (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.
doi: doi:10.1006/jdeq.1996.0009. |
show all references
References:
[1] |
M. Adimy and K. Ezzinbi, A class of linear partial neutral functional-differential equations with nondense domain,, J. Diff. Eqns., 147 (1998), 285.
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.
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.
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.
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.
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.
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.
|
[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.
doi: doi:10.1137/0512045. |
[9] |
Ph. Clément and J. Prüss, Global existence for a semilinear parabolic Volterra equation,, Math. Z., 209 (1992), 17.
doi: doi:10.1007/BF02570816. |
[10] |
R. Datko, Linear autonomous neutral differential equations in a Banach space,, J. Diff. Equations, 25 (1977), 258.
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.
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.
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,, Rocky Mountain J. Math., 25 (1995), 201.
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.
doi: doi:10.1007/BF00281373. |
[15] |
J. Hale and S. M. Verduyn Lunel, "Introduction to Functional-Differential Equations,", Applied Mathematical Sciences, 99 (1993).
|
[16] |
J. K. Hale, Partial neutral functional-differential equations,, Rev. Roumaine Math Pures Appl, 39 (1994), 339.
|
[17] |
H. Henriquez, Periodic solutions of abstract neutral functional differential equations with infinite delay,, Acta Math. Hungar., 121 (2008), 203.
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.
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.
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.
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.
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.
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.
|
[24] |
A. Lunardi, On the linear heat equation with fading memory,, SIAM J. Math. Anal., 21 (1990), 1213.
doi: doi:10.1137/0521066. |
[25] |
A. Lunardi., "Analytic Semigroups and Optimal Regularity in Parabolic Problems,", PNLDE, 16 (1995).
|
[26] |
J. W. Nunziato, On heat conduction in materials with memory,, Quart. Appl. Math., 29 (1971), 187.
|
[27] |
A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations,", Applied Mathematical Sciences, 44 (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.
doi: doi:10.1006/jdeq.1996.0009. |
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