IJPAM: Volume 68, No. 3 (2011)

A GENERALIZED RIEMANN-STIELTJES INTEGRAL
ON TIME SCALES AND DISCONTINUOUS
DYNAMICAL EQUATIONS

Luciano Barbanti$^1$, Berenice Camargo Damasceno$^2$,
Fábio Roberto Chavarette$^3$, José Manoel Balthazar$^4$
$^{1,2,3}$Department of Mathematics
Faculty of Engineering
São Paulo State University - UNESP
Ilha Solteira (SP), 15385-000, BRAZIL
$^1$e-mail: barbanti@mat.feis.unesp.br
$^2$e-mail: berenice@mat.feis.unesp.br
$^3$e-mail: fabioch@mat.feis.unesp.br
$^4$Department of Statistics, Applied Mathematics and Computation
Institute of Geology and Sciences
São Paulo State University - UNESP
Rio Claro (SP), 13506-700, BRAZIL
$^1$e-mail: jmbaltha@rc.unesp.br


Abstract. This paper is concerned with a generalization of the Riemann-Stieltjes integral on time scales for deal with some aspects of discontinuous dynamic equations in which Riemann-Stieltjes integral does not works.

Received: September 2, 2010

AMS Subject Classification: 26A42, 34C35, 26E70, 45B05

Key Words and Phrases: discontinuous dynamic systems, existence of solutions, Riemann-Stieltjes integral, time scales, Fredholm-Stieltjes integral equations

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 68
Issue: 3