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Differential equations where the derivative is taken with respect to a measure

Journal Article · · Sbornik. Mathematics
 [1]
  1. Institute of Mathematics, National Academy of Sciences of Armenia, Yerevan (Armenia)
This paper looks at ordinary differential equations (DE) containing the derivative of the unknown functions with respect to a measure {mu} which is continuous with respect to the Lebesgue measure. It is shown that the Cauchy problem for a linear normal system of DE with a {mu}-derivative is uniquely solvable. A necessary and sufficient condition is obtained for the solvability of an equation of Riccati type with a {mu}-derivative. It is related to a boundary-value problem for a linear system of DE. Using this condition a necessary and sufficient condition is obtained for a Volterra factorization to exist for linear operators that differ from the identity by an integral operator that is completely continuous in the space L{sub p}({mu}), 1{<=}p<+{infinity}. Bibliography: 12 titles.
OSTI ID:
21592564
Journal Information:
Sbornik. Mathematics, Journal Name: Sbornik. Mathematics Journal Issue: 2 Vol. 202; ISSN 1064-5616
Country of Publication:
United States
Language:
English

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