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)
Existence results for a damped second order abstract functional differential equation with impulses. (English) Zbl 1185.34113
Summary: We study the existence and regularity of mild solutions for a damped second order abstract functional differential equation with impulses. The results are obtained using the cosine function theory and fixed point criterions.
34K30Functional-differential equations in abstract spaces
34G10Linear ODE in abstract spaces
34K45Functional-differential equations with impulses
[1]Guo, D.; Liu, X.: A boundary value problem for second order impulsive integro-differential equations in a Banach space, Dynamics of continuous, discrete and impulsive systems series A: mathematical analysis 10, 1001-1016 (2003)
[2]Hernández, E.; Rabello, M.; Henríquez, H. R.: Existence of solutions for impulsive partial neutral functional differential equations, Journal of mathematical analysis and applications 331, 1135-1158 (2007) · Zbl 1123.34062 · doi:10.1016/j.jmaa.2006.09.043
[3]Lakshmikantham, V.; Bainov, D. D.; Simeonov, P. S.: Theory of impulsive differential equations, (1989) · Zbl 0718.34011
[4]Park, J. Y.; Balachandran, K.; Annapoorani, N.: Existence results for impulsive neutral functional integrodifferential equations with infinite delay, Nonlinear analysis 71, 3152-3162 (2009) · Zbl 1196.34105 · doi:10.1016/j.na.2009.01.192
[5]Rogovchenko, Y. V.: Impulsive evolution systems: Main results and new trends, Dynamics of continuous, discrete and impulsive systems 3, 57-88 (1997) · Zbl 0879.34014
[6]Samoilenko, A. M.; Perestyuk, N. A.: Impulsive differential equations, (1995) · Zbl 0837.34003
[7]Hernández, E.: A second-order impulsive Cauchy problem, International journal of mathematics and mathematical sciences 31, 451-461 (2002) · Zbl 1013.34061 · doi:10.1155/S0161171202012735
[8]Hernández, E.: Existence results for a partial second order functional differential equation with impulses, Dynamics of continuous, discrete and impulsive systems, series A: mathematical analysis 14, 229-250 (2007) · Zbl 1127.34049
[9]Hernández, E.; Henríquez, H. R.; Mckibben, M. A.: Existence results for abstract impulsive second-order neutral functional differential equations, Nonlinear analysis:Theory, methods and applications 70, 2736-2751 (2009) · Zbl 1173.34049 · doi:10.1016/j.na.2008.03.062
[10]Balachandran, K.; Park, J. Y.: Existence of solutions of second order nonlinear differential equations with nonlocal conditions in Banach spaces, Indian journal of pure and applied mathematics 32, 1883-1892 (2001) · Zbl 1006.34055
[11]Benchohra, M.; Henderson, J.; Ntouyas, S. K.; Ouahab, A.: Existence results for impulsive semilinear damped differential inclusions, Electronic journal of qualitative theory of differential equations, No. 11, 1-19 (2003) · Zbl 1046.34017 · doi:emis:journals/EJQTDE/2003/200311.html
[12]Lin, Y.; Tanaka, N.: Nonlinear abstract wave equations with strong damping, Journal of mathematical analysis and applications 225, 46-61 (1998) · Zbl 0918.35094 · doi:10.1006/jmaa.1998.5999
[13]Sandefur, J. T.: Existence and uniqueness of solutions of second order nonlinear differential equations, SIAM journal of mathematical analysis 14, 477-487 (1983) · Zbl 0513.34069 · doi:10.1137/0514041
[14]Webb, G. F.: Existence and asymptotic behaviour for a strongly damped nonlinear wave equations, Canadian journal of mathematics 32, 631-643 (1980) · Zbl 0414.35046 · doi:10.4153/CJM-1980-049-5
[15]Kisynski, J.: On cosine operator functions and one parameter group of operators, Studia Mathematica,l 49, 93-105 (1972) · Zbl 0232.47045
[16]Travis, C. C.; Webb, G. F.: Compactness, regularity and uniform continuity properties of strongly continuous cosine families, Houston journal of mathematics 3, 555-567 (1977) · Zbl 0386.47024
[17]Travis, C. C.; Webb, G. F.: Cosine families and abstract nonlinear second order differentials equations, Acta Mathematica academiae scientiarum hungaricae 32, 76-96 (1978) · Zbl 0388.34039 · doi:10.1007/BF01902205
[18]Henríquez, H. R.; Vasquez, C. H.: Differentiability of solutions of the second order abstract Cauchy problem, Semigroup forum 64, No. 3, 472-488 (2002) · Zbl 1032.47026 · doi:10.1007/s002330010092
[19]Granas, A.; Dugundji, J.: Fixed point thoery, (2003)
[20]Hernández, E.; Mckibben, M. A.: Some comments on : existence of solutions of abstract nonlinear second-order neutral functional integrodifferential equations, Computers and mathematics with applications 46, No. 8–9, 655-669 (2003) · Zbl 1054.45006 · doi:10.1016/S0898-1221(03)90221-5
[21]Martin, R. H.: Nonlinear operators and differential equations in Banach spaces, (1987) · Zbl 0649.47039
[22]Fattorini, H. O.: Second order linear differential equations in Banach spaces, (1985) · Zbl 0582.34048 · doi:10.1017/S0308210500020801