Nonlinear differential problems with first- or second-order differences in Hilbert spaces

In a real Hilbert space, we investigate the existence, uniqueness and asymptotic properties of the generalized solutions of some nonlinear differential systems with first- or second-order differences, subject to extreme conditions and initial data. Some generalizations of Minty’s theorem for the cha...

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Bibliographic Details
Published inNonlinear analysis Vol. 71; no. 12; pp. e81 - e97
Main Author Luca, Rodica
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 15.12.2009
Subjects
Asymptotic properties
Cauchy problem
Difference equation
Differential system
Extreme condition
Hilbert space
Maximal monotone operator
Nonlinearity
Operators
Strong solution
Theorems
Uniqueness
Weak solution
34G20
Weak solution
39A12
Differential system
Extreme condition
Maximal monotone operator
47H05
Strong solution
Difference equation
Cauchy problem
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ISSN0362-546X
1873-5215
DOI10.1016/j.na.2008.10.006

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Summary:In a real Hilbert space, we investigate the existence, uniqueness and asymptotic properties of the generalized solutions of some nonlinear differential systems with first- or second-order differences, subject to extreme conditions and initial data. Some generalizations of Minty’s theorem for the characterization of maximal monotone operators are also presented.
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ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2008.10.006