An abstract doubly nonlinear equation with a measure as initial value

The solvability of the abstract implicit nonlinear nonautonomous differential equation ( A ( t ) u ( t ) ) ′ + B ( t ) u ( t ) + C ( t ) u ( t ) ∋ f ( t ) will be investigated in the case of a measure as an initial value. It will be shown that this problem has a solution if the inner product of A (...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2007-07, Vol.331 (1), p.308-328
Main Authors: Aizicovici, Sergiu, Hokkanen, Veli-Matti
Format: Article
Language:English
Subjects:
Exact sciences and technology
Functional analysis
Global analysis, analysis on manifolds
Mathematical analysis
Mathematics
Maximal monotone operator
Nonlinear evolution equation
Ordinary differential equations
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary:The solvability of the abstract implicit nonlinear nonautonomous differential equation ( A ( t ) u ( t ) ) ′ + B ( t ) u ( t ) + C ( t ) u ( t ) ∋ f ( t ) will be investigated in the case of a measure as an initial value. It will be shown that this problem has a solution if the inner product of A ( t ) x and B ( t ) x + C ( t ) x is bounded below.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2006.08.074