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SOME OPIAL-TYPE INEQUALITIES APPLICABLE TO DIFFERENTIAL EQUATIONS INVOLVING IMPULSES
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  • Journal title : The Pure and Applied Mathematics
  • Volume 22, Issue 4,  2015, pp.315-331
  • Publisher : Korea Society of Mathematical Education
  • DOI : 10.7468/jksmeb.2015.22.4.315
 Title & Authors
SOME OPIAL-TYPE INEQUALITIES APPLICABLE TO DIFFERENTIAL EQUATIONS INVOLVING IMPULSES
KIM, YOUNG JIN;
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 Abstract
The purpose of this paper is to obtain Opial-type inequalities that are useful to study various qualitative properties of certain differential equations involving impulses. After we obtain some Opial-type inequalities, we apply our results to certain differential equations involving impulses.
 Keywords
Stieltjes derivatives;Opial-type inequalities;differential equations involv-ing impulses;
 Language
English
 Cited by
 References
1.
R.P. Agarwal & P.Y.H. Pang: Opial inequalities with applications in differential anddifference equations. Kluwer Academic Publishers, Dordrecht, 1995.

2.
R. Henstock: Lectures on the theory of integration. World Scientific, Singapore, 1988.

3.
C.S. Hönig : Volterra Stieltjes-integral equations. North Holand and American Elsevier, Mathematics Studies 16, Amsterdam and New York, 1973.

4.
Y.J. Kim: Stieltjes derivatives and its applications to integral inequalities of Stieltjes type. J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. 18 (2011), no. 1, 63-78.

5.
______: Stieltjes derivative method for integral inequalities with impulses. J. Korean Soc. Math. Educ.Ser. B: Pure Appl. Math. 21 (2014), no. 1, 61-75.

6.
P. Krejčí & J. Kurzweil: A nonexistence result for the Kurzweil integral. Math. Bohem. 127 (2002), 571-580.

7.
W.F. Pfeffer: The Riemann approach to integration: local geometric theory. Cambridge Tracts in Mathematics 109, Cambridge University Press, 1993.

8.
A.M. Samoilenko & N.A. Perestyuk: Impulsive differential equations. World Scientific, Singapore, 1995.

9.
Š. Schwabik: Generalized ordinary differential equations. World Scientific, Singapore, 1992.

10.
Š. Schwabik, M. Tvrdý & O. Vejvoda: Differntial and integral equations: boundary value problems and adjoints. Academia and D. Reidel, Praha and Dordrecht, 1979.

11.
M. Tvrdý : Regulated functions and the Perron-Stieltjes integral. Časopis pešt. mat. 114 (1989), no. 2, 187-209.