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SOME OPIAL-TYPE INEQUALITIES APPLICABLE TO DIFFERENTIAL EQUATIONS INVOLVING IMPULSES

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2015, v.22 no.4, pp.315-331
https://doi.org/10.7468/jksmeb.2015.22.4.315
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

Reference

1.

Schwabik, Š.;. Generalized ordinary differential equations.

2.

Samoilenko, A.M.;Perestyuk, N.A.;. Impulsive differential equations.

3.

Pfeffer, W.F.;. The Riemann approach to integration: local geometric theory.

4.

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

5.

Kim, Y.J.;. (2014). Stieltjes derivative method for integral inequalities with impulses. J. Korean Soc. Math. Educ.Ser. B: Pure Appl. Math., 21(1), 61-75.

6.

Kim, Y.J.;. (2011). Stieltjes derivatives and its applications to integral inequalities of Stieltjes type. J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math., 18(1), 63-78.

7.

Hönig, C.S.;. Volterra Stieltjes-integral equations.

8.

Henstock, R.;. Lectures on the theory of integration.

9.

Agarwal, R.P.;Pang, P.Y.H.;. Opial inequalities with applications in differential anddifference equations.

10.

Tvrdý, M.;. (1989). Regulated functions and the Perron-Stieltjes integral. Časopis pešt. mat., 114(2), 187-209.

11.

Schwabik, Š.;Tvrdý, M.;Vejvoda, O.;. Differntial and integral equations: boundary value problems and adjoints.

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics