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A Trotter-Kato type result for a second order difference inclusion in a Hilbert space. (English) Zbl 1181.47066

A Trotter-Kato type result is proved for the following boundary value problem:

u i+1 -(1+θ i )u i +θ i u i-1 c i Au i +f i (i=1,2,),
u 1 -u 0 α(u 0 -a),

where A and α are nonlinear maximal monotone operators (possibly multivalued) in a real Hilbert space, a,f i and c i >0,0<θ i <1 (i=1,2,)·

MSC:
47J22Variational and other types of inclusions
47H05Monotone operators (with respect to duality) and generalizations
References:
[1]Aftabizadeh, A.; Pavel, N.: Nonlinear boundary value problems for some ordinary and partial differential equations associated with monotone operators, J. math. Anal. appl. 156, 535-557 (1991) · Zbl 0734.34060 · doi:10.1016/0022-247X(91)90413-T
[2]Apreutesei, G.: Set convergence and the class of compact subsets, An. stiint. Univ. al. I. cuza iasi 47, No. 2, 263-276 (2001) · Zbl 1059.54506
[3]Apreutesei, G.: Families of subsets and the coincidence of hypertopologies, An. stiint. Univ. al. I. cuza iasi 49, No. 1, 3-18 (2003) · Zbl 1059.54508
[4]Apreutesei, N.: Second order differential equations on half-line associated with monotone operators, J. math. Anal. appl. 223, 472-493 (1998) · Zbl 0920.34025 · doi:10.1006/jmaa.1998.5960
[5]Apreutesei, N.: On a class of difference equations of monotone type, J. math. Anal. appl. 288, 833-851 (2003) · Zbl 1040.39002 · doi:10.1016/j.jmaa.2003.09.017
[6]Apreutesei, N.: Existence and equivalence with an optimization problem for some difference inclusions, Nonlinear anal. 57, No. 5 – 6, 795-813 (2004) · Zbl 1056.39001 · doi:10.1016/j.na.2004.03.018
[7]Apreutesei, N.: Continuous dependence on data for quasi-autonomous nonlinear boundary value problems, Abstr. appl. Anal. 1, 67-86 (2005) · Zbl 1086.34054 · doi:10.1155/AAA.2005.67
[8]Apreutesei, N.: Nonlinear second order evolution equations of monotone type and applications, (2007)
[9]Apreutesei, N.; Dimitriu, G.: Solving the second order evolution equations by internal schemes of approximation, Lecture notes in comput. Sci. 4310, 516-524 (2007)
[10]Attouch, H.: Variational convergence for functions and operators, (1984) · Zbl 0561.49012
[11]Banasiak, J.; Lachowicz, M.; Moszynski, M.: Semigroups for generalized birth-and-death equations in lp spaces, Semigroup forum 73, 175-193 (2006) · Zbl 1178.47027 · doi:10.1007/s00233-006-0621-x
[12]Barbu, V.: A class of boundary problems for second order abstract differential equations, J. fac. Sci. univ. Tokyo 19, 295-319 (1972) · Zbl 0256.47052
[13]Barbu, V.: Nonlinear semigroups and differential equations in Banach spaces, (1976)
[14]Bobrowski, A.: On limitations and insufficiency of the Trotter – Kato theorem, Semigroup forum 75, No. 2, 317-336 (2007) · Zbl 1132.47032 · doi:10.1007/s00233-006-0676-4
[15]Brézis, H.: Opérateurs maximaux monotones et semi-groupes de contractions dans LES espaces de Hilbert, (1973)
[16]Brézis, H.; Pazy, A.: Convergence and approximation of semigroups of nonlinear operators in Banach spaces, J. funct. Anal. 9, 63-74 (1972) · Zbl 0231.47036 · doi:10.1016/0022-1236(72)90014-6
[17]Kobayashi, Y.; Tanaka, N.: Convergence and approximation of semigroups of Lipschitz operators, Nonlinear anal. 61, No. 5, 781-821 (2005) · Zbl 1078.47023 · doi:10.1016/j.na.2005.01.040
[18]Ma, H.; Xue, X.: Second order nonlinear multivalued boundary problems in Hilbert spaces, J. math. Anal. appl. 303, No. 2, 736-753 (2005) · Zbl 1067.34064 · doi:10.1016/j.jmaa.2004.09.001
[19]Bachar, Mardiyana M.; Desch, W.: A Trotter – Kato theorem for α-times integrated C-regularized semigroups, Funct. differ. Equ. 11, No. 1 – 2, 103-110 (2004) · Zbl 1076.47030
[20]Pavel, N.: Nonlinear evolution operators and semigroups, applications to partial differential equations, Lecture notes in math. 1260 (1987) · Zbl 0626.35003
[21]Poffald, E.; Reich, S.: An incomplete Cauchy problem, J. math. Anal. appl. 113, 514-543 (1986) · Zbl 0599.34078 · doi:10.1016/0022-247X(86)90323-9
[22]Reich, S.; Shafrir, I.: An existence theorem for a difference inclusion in general Banach spaces, J. math. Anal. appl. 160, 406-412 (1991) · Zbl 0813.47041 · doi:10.1016/0022-247X(91)90313-O
[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 · Zbl 1143.34041 · doi:10.1155/2007/72931
[24]Rouhani, B. D.; Khatibzadeh, H.: A note on the asymptotic behavior of solutions to a second order difference equations, J. difference equ. Appl. 14, No. 4, 429-432 (2008) · Zbl 1138.39013 · doi:10.1080/10236190701825162