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.

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

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

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