HÖLDER CONTINUOUS SOLUTIONS FOR SECOND ORDER INTEGRO-DIFFERENTIAL EQUATIONS IN BANACH SPACES

doi:10.1016/S0252-9602(11)60274-9

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (3): 765-777.doi: 10.1016/S0252-9602(11)60274-9

HÖLDER CONTINUOUS SOLUTIONS FOR SECOND ORDER INTEGRO-DIFFERENTIAL EQUATIONS IN BANACH SPACES

Department of Mathematical Science, University of Tsinghua, Beijing 100084, China

收稿日期:2008-10-21 修回日期:2009-11-19 出版日期:2011-05-20 发布日期:2011-05-20
基金资助:
This work was supported by the NSF of China and the Specialized Research Fund for the Doctoral Program of Higher Education.

HÖLDER CONTINUOUS SOLUTIONS FOR SECOND ORDER INTEGRO-DIFFERENTIAL EQUATIONS IN BANACH SPACES

Department of Mathematical Science, University of Tsinghua, Beijing 100084, China

Received:2008-10-21 Revised:2009-11-19 Online:2011-05-20 Published:2011-05-20
Supported by:
This work was supported by the NSF of China and the Specialized Research Fund for the Doctoral Program of Higher Education.

摘要/Abstract

摘要：

We study H\"older continuous solutions for the second order integro-differential equations with infinite delay (P₁): u''(t)+ cu'(t)+∫^t_-∞β (t-s)u'(s)ds+∫^t_-∞γ(t-s)u(s)ds =Au(t)-∫^t_-∞δ(t-s)Au(s)ds+f(t) on the line R, where 0 < α< 1, A is a closed operator in a complex Banach space X, c ∈C is a constant, f ∈C^α (R，X) and β, γ, δ ∈L¹(R₊). Under suitable assumptions on the kernels β, γ and δ, we completely characterize the C^α-well-posedness of (P₁) by using operator-valued C^α-Fourier multipliers.

关键词: Fourier multiplier, C^α-well-posedness, integro-differential equations

Abstract:

Key words: Fourier multiplier, C^α-well-posedness, integro-differential equations

中图分类号:

45N05

步尚全. HÖLDER CONTINUOUS SOLUTIONS FOR SECOND ORDER INTEGRO-DIFFERENTIAL EQUATIONS IN BANACH SPACES[J]. 数学物理学报(英文版), 2011, 31(3): 765-777.

BU Shang-Quan. HÖLDER CONTINUOUS SOLUTIONS FOR SECOND ORDER INTEGRO-DIFFERENTIAL EQUATIONS IN BANACH SPACES[J]. Acta mathematica scientia,Series B, 2011, 31(3): 765-777.

参考文献

[1] Arendt W, Bu S. The operator-valued Marcinkiewicz multiplier theorem and maximal regularity. Math Z, 2002, 240: 311--343

[2] Arendt W, Bu S. Operator-valued Fourier multipliers on periodic Besov spaces and applications. Proc Edinb Math Soc, 2004, 47: 15--33

[3] Arendt W, Batty C, Bu S. Fourier multipliers for H\"older continuous functions and maximal regularity. Studia Math, 2004, 160: 23--51

[4] Brèzis H. Analyse Fonctionnelle. Paris: Masson, 1983

[5]  Bu S, Kim J. Operator-valued Fourier multipliers on periodic Triebel spaces. Acta Math Sinica, English Series, 2005, 21(5): 1049--1056

[6]  Bu S, Fang Y. Periodic solutions for second order integro-differential equations with infinite delay in Banach spaces. Studia Mathematica, 2008, 184(2): 103--1119

[7] Chill R, Srivastava S. L^p-maximal regularity for second order Cauchy problems. Math Z, 2005, 251: 751--781

[8] Clèment Ph, Da Prato G. Existence and regularity results for an integral equation with infinite delay in a Banach space. Int Equ Ope The, 1988, 11: 480--550

[9]  Da Prato G, Lunardi A. Solvability on the real line of a class of linear Volterra integro-differential equations of parabolic type. Ann Mat Pura Appl, 1988, 150(4): 67--117

[10] Keyantuo V, Lizama C. H\"older continuous solutions for integro-differential equations and maximal regularity. J Differ Equ, 2006, 230: 634--660

[11] Keyantuo V,  Lizama C. Fourier multipliers and integro-differential equations in Banach spaces. J London Math Soc, 2004, 69(2): 737--750

[12] Keyantuo V, Lizama C. Maximal regularity for a class of integro-differential equations with infinite delay in Banach spaces. Studia Math, 2005, 168(1): 25--50

[13] Lunardi A. The heat equation with fading memory. SIAM J Math Anal, 1990, 21: 1213--1224

[14] Weis L. Operator-valued Fourier multipliers and maximal L^p-regularity. Math Ann, 2001, 319: 735--758

[15] Weis L. A new approach to maximal L^p-regularity//Evolution Equations and Their Applications in Physical and Life Sciences (Bad Herrenalb, 1998), Lecture Notes in Pure and Appl Math 215. New York: Dekker, 2001: 195--214

HÖLDER CONTINUOUS SOLUTIONS FOR SECOND ORDER INTEGRO-DIFFERENTIAL EQUATIONS IN BANACH SPACES

HÖLDER CONTINUOUS SOLUTIONS FOR SECOND ORDER INTEGRO-DIFFERENTIAL EQUATIONS IN BANACH SPACES

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 8

Metrics

本文评价

推荐阅读 0

[1]	Shangquan BU, Gang CAI. THE WELL-POSEDNESS OF FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS IN COMPLEX BANACH SPACES^∗[J]. 数学物理学报(英文版), 2023, 43(4): 1603-1617.
[2]	何骞君, 吴新峰, 燕敦验. BOUNDS FOR MULTILINEAR OPERATORS UNDER AN INTEGRAL TYPE CONDITION ON MORREY SPACES[J]. 数学物理学报(英文版), 2022, 42(3): 1191-1208.
[3]	陈吕萍. THE APPROXIMATION SOLUTIONS FOR HIGHER DIMENSIONAL INTEGRO-DIFFERENTIAL EQUATIONS[J]. 数学物理学报(英文版), 2019, 39(5): 1309-1318.
[4]	马和平, 刘斌. EXACT CONTROLLABILITY AND CONTINUOUS DEPENDENCE OF FRACTIONAL NEUTRAL INTEGRO-DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY[J]. 数学物理学报(英文版), 2017, 37(1): 235-258.
[5]	Dimplekumar N. CHALISHAJAR, K. KARTHIKEYAN. EXISTENCE AND UNIQUENESS RESULTS FOR BOUNDARY VALUE PROBLEMS OF HIGHER ORDER FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS INVOLVING GRONWALL´S INEQUALITY IN BANACH SPACES[J]. 数学物理学报(英文版), 2013, 33(3): 758-772.
[6]	牛原玲, 张诚坚, 段金桥. A DELAY-DEPENDENT STABILITY CRITERION FOR NONLINEAR STOCHASTIC DELAY-INTEGRO-DIFFERENTIAL EQUATIONS[J]. 数学物理学报(英文版), 2011, 31(5): 1813-1822.
[7]	Veli Shakhmurov. ABSTRACT CAPACITY OF REGIONS AND COMPACT EMBEDDING WITH APPLICATIONS[J]. 数学物理学报(英文版), 2011, 31(1): 49-67.
[8]	孙澎涛. MIXED FINITE ELEMENTS FOR PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS[J]. 数学物理学报(英文版), 1997, 17(3): 319-329.