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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| Published in | Nonlinear analysis Vol. 71; no. 12; pp. e81 - e97 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
15.12.2009
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0362-546X 1873-5215 |
| DOI | 10.1016/j.na.2008.10.006 |
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| Abstract | 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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| AbstractList | 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. |
| Author | Luca, Rodica |
| Author_xml | – sequence: 1 givenname: Rodica surname: Luca fullname: Luca, Rodica email: rluca@math.tuiasi.ro, rlucatudor@yahoo.com organization: Department of Mathematics, Gh. Asachi Technical University, 11 Blvd. Carol I, Iaşi 700506, Romania |
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| Cites_doi | 10.1016/0022-247X(68)90038-3 10.1090/conm/371/06858 10.3233/ASY-2007-808 10.1016/0022-247X(81)90136-0 10.1016/0362-546X(81)90019-5 10.2969/jmsj/01940508 10.57262/die/1369055617 10.1016/j.na.2006.09.003 10.1016/0362-546X(81)90039-0 10.1016/j.jmaa.2006.06.048 |
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| Keywords | 34G20 Weak solution 39A12 Differential system Extreme condition Maximal monotone operator 47H05 Strong solution Difference equation Cauchy problem |
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| References | Luca (b18) 2007; 67 Lakshmikantham, Leela (b13) 1981; vol. 2 Luca (b19) 2007; 329 R. Luca, On a class of nonlinear boundary value problems, Int. J. Appl. Math. Sci. (in press) Agarwal, Wong (b2) 1997; vol. 404 Attouch (b3) 1981; 5 Luca (b15) 1999; 1 Luca (b14) 1995; 8 Luca (b17) 2006; 32 Agarwal (b1) 2000; vol. 228 A. Rousseau, R. Temam, J. Tribbia, Boundary conditions for an ocean related system with a small parameter, in: Nonlinear Partial Differential Equations and Related Analysis, Contemp. Math. 371 (2005) 231–263 Barbu (b4) 1976 Luca (b21) 2007; 40 Moroşanu, Petrovanu (b25) 1985–1986; 34 Cooke, Krumme (b8) 1968; 24 Luca (b20) 2007; 51 Barbu, Moroşanu (b6) 1981; 5 Moroşanu (b24) 1988 Barbu (b5) 1977; 22 Luca (b16) 2004; 8 Moroşanu (b23) 1981; 83 Brezis (b7) 1973 Halanay, Răzvan (b9) 1979; 24 Kato (b11) 1967; 19 Ladde, Lakshmikantham, Vatsalo (b12) 1985; vol. 27 Iftimie (b10) 1976; 21 Agarwal (10.1016/j.na.2008.10.006_b1) 2000; vol. 228 Luca (10.1016/j.na.2008.10.006_b15) 1999; 1 Luca (10.1016/j.na.2008.10.006_b18) 2007; 67 Barbu (10.1016/j.na.2008.10.006_b4) 1976 Attouch (10.1016/j.na.2008.10.006_b3) 1981; 5 Kato (10.1016/j.na.2008.10.006_b11) 1967; 19 Ladde (10.1016/j.na.2008.10.006_b12) 1985; vol. 27 Luca (10.1016/j.na.2008.10.006_b20) 2007; 51 10.1016/j.na.2008.10.006_b22 Luca (10.1016/j.na.2008.10.006_b14) 1995; 8 10.1016/j.na.2008.10.006_b26 Luca (10.1016/j.na.2008.10.006_b19) 2007; 329 Moroşanu (10.1016/j.na.2008.10.006_b24) 1988 Luca (10.1016/j.na.2008.10.006_b21) 2007; 40 Agarwal (10.1016/j.na.2008.10.006_b2) 1997; vol. 404 Barbu (10.1016/j.na.2008.10.006_b6) 1981; 5 Lakshmikantham (10.1016/j.na.2008.10.006_b13) 1981; vol. 2 Barbu (10.1016/j.na.2008.10.006_b5) 1977; 22 Cooke (10.1016/j.na.2008.10.006_b8) 1968; 24 Moroşanu (10.1016/j.na.2008.10.006_b25) 1985; 34 Brezis (10.1016/j.na.2008.10.006_b7) 1973 Halanay (10.1016/j.na.2008.10.006_b9) 1979; 24 Luca (10.1016/j.na.2008.10.006_b17) 2006; 32 Iftimie (10.1016/j.na.2008.10.006_b10) 1976; 21 Luca (10.1016/j.na.2008.10.006_b16) 2004; 8 Moroşanu (10.1016/j.na.2008.10.006_b23) 1981; 83 |
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| SubjectTerms | Asymptotic properties Cauchy problem Difference equation Differential system Extreme condition Hilbert space Maximal monotone operator Nonlinearity Operators Strong solution Theorems Uniqueness Weak solution |
| Title | Nonlinear differential problems with first- or second-order differences in Hilbert spaces |
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