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)
Generalization of a retarded Gronwall-like inequality and its applications. (English) Zbl 1078.26010
In the present paper, an explicit bound on the generalization of a certain retarded integral inequality is given. Some applications are given to illustrate the usefulness of the result.

26D10Inequalities involving derivatives, differential and integral operators
Full Text: DOI
[1] Bellman, R.: Stability theory of differential equations. (1953) · Zbl 0053.24705
[2] Bihari, I. A.: A generalization of a lemma of Bellman and its application to uniqueness problem of differential equation. Acta math. Acad. sci. Hung. 7, 81-94 (1956) · Zbl 0070.08201
[3] Dannan, F.: Integral inequalities of Gronwall-Bellman-bihari type and asymptotic behavior of certain second order nonlinear differential equations. J. math. Anal. appl. 108, 151-164 (1985) · Zbl 0586.26008
[4] Driver, R.: Existence and continuous dependence of solutions of neutral functional differential equations. Arch. rational mech. Anal. 19, 149-166 (1965) · Zbl 0148.05703
[5] Hale, J. K.: Theory of functional differential equations. (1977) · Zbl 0352.34001
[6] Lakshmikantham, V.; Rao, M. R. M.: Theory of integro-differential equations. (1995) · Zbl 0849.45004
[7] Lipovan, O.: A retarded Gronwall-like inequality and its applications. J. math. Anal. appl. 252, 389-401 (2000) · Zbl 0974.26007
[8] Medina, R.; Pinto, M.: On the asymptotic behavior of solutions of a class of second order nonlinear differential equations. J. math. Anal. appl. 135, 399-405 (1988) · Zbl 0668.34056
[9] Pachpatte, B. G.: A note on Gronwall-Bellman inequality. J. math. Anal. appl. 44, 758-762 (1973) · Zbl 0274.45011
[10] Pachpatte, B. G.: On some generalization of Bellman’s lemma. J. math. Anal. appl. 51, 141-150 (1975) · Zbl 0305.26010
[11] Pachpatte, B. G.: Inequalities for differential and integral equations. (1998) · Zbl 1032.26008
[12] Pinto, M.: Perturbations of asymptotically stable differential systems. Analysis 4, 161-175 (1984) · Zbl 0568.34035
[13] Pinto, M.: Integral inequalities of bihari-type and applications. Funkcial. ekvac. 33, 387-403 (1990) · Zbl 0717.45004
[14] Zhang, W.: Generalized exponential dichotomies and invariant manifolds for differential equations. Adv. math. Chin. 22, 1-45 (1993) · Zbl 0791.34039