Acta mathematica scientia, Series B >
HÖLDER CONTINUOUS SOLUTIONS FOR SECOND ORDER INTEGRO-DIFFERENTIAL EQUATIONS IN BANACH SPACES
Received date: 2008-10-21
Revised date: 2009-11-19
Online 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.
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 ∈Cα (R，X) and β, γ, δ ∈L1(R+). Under suitable assumptions on the kernels β, γ and δ, we completely characterize the Cα-well-posedness of (P1) by using operator-valued Cα-Fourier multipliers.
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 . DOI: 10.1016/S0252-9602(11)60274-9
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