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ON SOME GRONWALL TYPE INTEGRAL INEQUALITIES AND THEIR APPLICATIONS
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 Title & Authors
ON SOME GRONWALL TYPE INTEGRAL INEQUALITIES AND THEIR APPLICATIONS
Kim, Byung-Il;
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 Abstract
The aim of the present paper is to establish some nonlinear integral inequalities in two independent variables which provide explicit bounds on unknown functions. The inequalities given here can be used as tools in the qualitative theory of certain partial differential equations.
 Keywords
integral inequality;two independent variables;partial differential equations;nondecreasing;nonincreasing;
 Language
English
 Cited by
1.
On some new integral inequalities of Gronwall–Bellman–Pachpatte type, Applied Mathematics and Computation, 2011, 217, 20, 7887  crossref(new windwow)
 References
1.
D. Bainov and P. Simeonov, Integral Inequalities and Applications, Kluwer Academic Publishers, Dordrecht, 1992

2.
E. F. Beckenbach and R. Bellman, Inequalities, Springer-Verlag, New York, 1961

3.
R. Bellman, The stability of solutions of linear differential equations, Duke Math. J. 10 (1943), 643–647

4.
I. Bihari, A generalization of a lemma of Bellman and its application to uniqueness problems of differential equations, Acta Math. Acad. Sci. Hungar. 7 (1956), 71–94

5.
S. S. Dragomir and N. M. Ionescu, On nonlinear integral inequalities in two independent variables, Stud. Univ. Babe¸s-Bolyai Math. 34 (1989), 11–17

6.
S. S. Dragomir and Y. -H. Kim, On certain new integral inequalities and their applications, J. Inequal. Pure Appl. Math. 3 (2002), no. 4, 1–8

7.
S. S. Dragomir and Y. -H. Kim, Some integral inequalities for function of two variables, Electron. J. Differential Equations 2003 (2003), no. 10, 1–13

8.
T. H. Gronwall, Note on the derivatives with respect to a parameter of solutions of a system of differential equations, Ann. of Math. 20 (1919), 292–296

9.
L. Guiliano, Generalazzioni di un lemma di Gronwall, Rend. Accad., Lincei, 1946, pp. 1264–1271

10.
C. E. Langenhop, Bounds on the norm of a solution of a general differential equation, Proc. Amer. Math. Soc. 11 (1960), 795–799

11.
A. Mate and P. Neval, Sublinear perturbations of the differential equation $Y^{(n)}$ = 0 and of the analogous difference equation, J. Differential Equations 52 (1984), 234–257

12.
D. S. Mitrinovic, J. E. Peˇcari´c and A. M. Fink, Inequalities Involving Functions and Their Integrals and Derivatives, Kluwer Academic Publishers, Dordrecht, Boston, London, 1991

13.
V. V. Nemyckii and V. V. Stepanov, Qualitative theory of differential equations (Russian), OGIZ, Moscow, 1947

14.
B. G. Pachpatte, On some fundamental integral inequalities and their discrete analogues, J. Inequal. Pure Appl. Math. 2 (2001), no. 2, 1–13