Schwabik S. Generalized Ordinary Differential Equations

World Scientific, 1992. - 392 Pages.The intention of this book is to survey some topics related to the study of ordinary differential equations in connection with the theory of nonabsolutely convergent integral.
Although the nonabsolutely convergent Perron integral is present in mathematics from the second decade of our century, the main step to establish this connection was done by Jaroslav Kurzweil (1957) and Ralph Henstock (1961) when they independently arrived at a construction of the Perron integral which is a simple extension of the Riemann theory of integration based on lucid and transparent Riemann integral sums. The approach of J. Kurzweil presented in and in the subsequent papers shows how the new approach to the general integration theory was growing up from the needs of ordinary differential equations. In particular, the presence of rapidly oscillating external forces was the main impulse for introducing a nonabsolutely convergent integral into the theory of ordinary differential equations instead of the Lebesgue integral or the classical Riemann integral.