zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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,)·

47J22Variational and other types of inclusions
47H05Monotone operators (with respect to duality) and generalizations
[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