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DOI QR Code

GENERALIZED SECOND-ORDER DIFFERENTIAL EQUATIONS WITH TWO-POINT BOUNDARY CONDITIONS

Kim, Young Jin

  • Received : 2018.07.11
  • Accepted : 2019.08.14
  • Published : 2019.08.31

Abstract

In this paper we define higher-order Stieltjes derivatives, and using Schaefer's fixed point theorem we investigate the existence of solutions for a class of differential equations involving second-order Stieltjes derivatives with two-point boundary conditions. The equations include ordinary and impulsive differential equations, and difference equations.

Keywords

higher-order Stieltjes derivatives;second-order differential equations;two-point boundary conditions

References

  1. D. Frankova: Regulated functions. Math. Bohem. 116 (1991), 20-59.
  2. J. Henderson & R. Luca: Boundary value problems for systems of differential, difference and fractional equations: positive solutions. Elsevier, Amsterdam, 2016.
  3. C.S. Honig: Volterra Stieltjes-integral equations. Mathematics Studies 16, North-Holand and American Elsevier, 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. Y.J. Kim: 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. Y.J. Kim: Some retarded integral inequalities and their applications. J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. 23(2016), no. 2, 181-199.
  7. Y.J. Kim: Asymptotic behavior of a certain second-order integro-differential equation. J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. 24 (2017), no. 1, 1-19.
  8. P. Krejci & J. Kurzweil: A nonexistence result for the Kurzweil integral. Math. Bohem. 127 (2002), 571-580.
  9. W.F. Pfeffer: The Riemann approach to integration: local geometric theory. Cambridge Tracts in Mathematics 109, Cambridge University Press, 1993.
  10. S. Schwabik: Generalized ordinary differential equations. World Scientific, Singapore, 1992.
  11. S. Schwabik, M. Tvrdy & O. Vejvoda: Differential and integral equations: boundary value problems and adjoints. Academia and D. Reidel, Praha and Dordrecht, 1979.
  12. D.R. Smart: Fixed point theorems. Cambridge University Press, London, 1980.
  13. M. Tvrdy: Regulated functions and the Perron-Stieltjes integral. Casopis pest. mat. 114 (1989), no. 2, 187-209.