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On a class of
differential equations for vector-valued distributions
Hector O. Fattorini |
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Vol. 32 (1970), No. 1, 79–104
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Abstract |
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The aim of this paper is to seek necessary and sufficient conditions on the linear operator A in a linear topological space in order that the Cauchy problem for the equation U(α) − AU = T should be well set in the sense of distributions (see definition in §2). Here 0 < α < ∞,U(α) is the fractional derivative of U of order α. Such conditions are obtained for α integer ≧ 3 and then for any α > 0, this time with the additional assumption of (at most) exponential growth of the solutions at infinity. |
Mathematical Subject Classification 2000
Primary: 35R99
Secondary: 47D05
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Milestones
Received: 1 July 1968
Revised: 28 October 1968
Published: 1 January 1970
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Authors |
| Hector O. Fattorini | |
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