A Trotter-Kato type result for a second order difference inclusion in a Hilbert space

Journal of Mathematical Analysis and Applications

Volumn 361, Issue 1, 2010, Pages 195-204

  Apreutesei, N ^a   Apreutesei, G ^b  

^a GHEORGHE ASACHI TECHNICAL UNIVERSITY OF IASI   (Romania)

^b ALEXANDRU IOAN CUZA UNIVERSITY OF IASI   (Romania)

Author keywords

Convergence in the sense of resolvent; Maximal monotone operator; Strongly monotone operator; The resolvent of an operator; Yosida approximation

Indexed keywords

EID: 70349399016     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2009.08.065     Document Type: Article

References (24)

1. Aftabizadeh A., and Pavel N. Nonlinear boundary value problems for some ordinary and partial differential equations associated with monotone operators. J. Math. Anal. Appl. 156 (1991) 535-557
2. Apreutesei G. Set convergence and the class of compact subsets. An. Stiint. Univ. Al. I. Cuza Iasi 47 2 (2001) 263-276
3. Apreutesei G. Families of subsets and the coincidence of hypertopologies. An. Stiint. Univ. Al. I. Cuza Iasi 49 1 (2003) 3-18
4. Apreutesei N. Second order differential equations on half-line associated with monotone operators. J. Math. Anal. Appl. 223 (1998) 472-493
5. Apreutesei N. On a class of difference equations of monotone type. J. Math. Anal. Appl. 288 (2003) 833-851
6. Apreutesei N. Existence and equivalence with an optimization problem for some difference inclusions. Nonlinear Anal. 57 5-6 (2004) 795-813
7. Apreutesei N. Continuous dependence on data for quasi-autonomous nonlinear boundary value problems. Abstr. Appl. Anal. 1 (2005) 67-86
8. Apreutesei N. Nonlinear Second Order Evolution Equations of Monotone Type and Applications (2007), Pushpa Publishing House, India
9. Apreutesei N., and Dimitriu G. Solving the second order evolution equations by internal schemes of approximation. Lecture Notes in Comput. Sci. vol. 4310 (2007), Springer, Berlin 516-524
10. Attouch H. Variational Convergence for Functions and Operators (1984), Pitman, Boston/London
11. p spaces. Semigroup Forum 73 (2006) 175-193
12. Barbu V. A class of boundary problems for second order abstract differential equations. J. Fac. Sci. Univ. Tokyo 19 (1972) 295-319
13. Barbu V. Nonlinear Semigroups and Differential Equations in Banach Spaces (1976), Noordhoff, Leyden
14. Bobrowski A. On limitations and insufficiency of the Trotter-Kato theorem. Semigroup Forum 75 2 (2007) 317-336
15. Brézis H. Opérateurs Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert (1973), North-Holland, Amsterdam
16. Brézis H., and Pazy A. Convergence and approximation of semigroups of nonlinear operators in Banach spaces. J. Funct. Anal. 9 (1972) 63-74
17. Kobayashi Y., and Tanaka N. Convergence and approximation of semigroups of Lipschitz operators. Nonlinear Anal. 61 5 (2005) 781-821
18. Ma H., and Xue X. Second order nonlinear multivalued boundary problems in Hilbert spaces. J. Math. Anal. Appl. 303 2 (2005) 736-753
19. Bachar M.M., and Desch W. A Trotter-Kato theorem for α-times integrated C-regularized semigroups. Funct. Differ. Equ. 11 1-2 (2004) 103-110
20. Pavel N. Nonlinear Evolution Operators and Semigroups, Applications to Partial Differential Equations. Lecture Notes in Math. vol. 1260 (1987), Springer-Verlag, New York, Berlin
21. Poffald E., and Reich S. An incomplete Cauchy problem. J. Math. Anal. Appl. 113 (1986) 514-543
22. Reich S., and Shafrir I. An existence theorem for a difference inclusion in general Banach spaces. J. Math. Anal. Appl. 160 (1991) 406-412
23. B.D. Rouhani, H. Khatibzadeh, Asymptotic behavior of solutions to some homogeneous second-order evolution equations of monotone type, J. Inequal. Appl. (2007), article ID 72931, 8 pages
24. Rouhani B.D., and Khatibzadeh H. A note on the asymptotic behavior of solutions to a second order difference equations. J. Difference Equ. Appl. 14 4 (2008) 429-432