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MILD WELL-POSEDNESS OF SECOND ORDER DIFFERENTIAL EQUATIONS ON THE REAL LINE

Shangquan Bu and Gang Cai
Taiwanese Journal of Mathematics
Vol. 17, No. 1 (February 2013), pp. 143-159
Stable URL: http://www.jstor.org/stable/taiwjmath.17.1.143
Page Count: 17
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MILD WELL-POSEDNESS OF SECOND ORDER DIFFERENTIAL EQUATIONS ON THE REAL LINE
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Abstract

Abstract We study the (W2,p, W1,p)-mild well-posedness of the second order differential equation (P2) : u″ = Au + f on the real line ℝ, where A is a densely defined closed operator on a Banach space X. We completely characterize the (W2,p, W1,p)-mild well-posedness of (P2) by Lp-Fourier multipliers defined by the resolvent of A. 2010 Mathematics Subject Classification: 47D06, 47A50, 42A45, 34K30. Key words and phrases: Second order differential equations, Mild well-posedness, Lp-Fourier multipliers.

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