0471069 - MÚ 2018 RIV HU eng J - Článek v odborném periodiku
Monteiro, Giselle Antunes - Satco, B. R.
Distributional, differential and integral problems: Equivalence and existence results.
Electronic Journal of Qualitative Theory of Differential Equations. Roč. 2017, č. 7 (2017), s. 1-26. ISSN 1417-3875. E-ISSN 1417-3875
Institucionální podpora: RVO:67985840
Klíčová slova: derivative with respect to functions * distribution * Kurzweil-Stieltjes integral
Obor OECD: Pure mathematics
Impakt faktor: 0.881, rok: 2017 ; AIS: 0.34, rok: 2017
Web výsledku:
http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=4753DOI: https://doi.org/10.14232/ejqtde.2017.1.7

We are interested in studying the matter of equivalence of the following problems: Dx = f (t, x)Dg x(0) = x0 (1) where Dx and Dg stand for the distributional derivatives of x and g, respectively, x'g(t) = f (t, x(t)), mg-a.e. x(0) = x0 (2) where x'g denotes the g-derivative of x (in a sense to be specified in Section 2) and mg is the variational measure induced by g, and x(t) = x0 + ...t 0 f (s, x(s))dg(s), (3) where the integral is understood in the Kurzweil-Stieltjes sense. We prove that, for regulated functions g, (1) and (3) are equivalent if f satisfies a bounded variation assumption. The relation between problems (2) and (3) is described for very general f, though, more restrictive assumptions over the function g are required. We provide then two existence results for the integral problem (3) and, using the correspondences established with the other problems, we deduce the existence of solutions for (1) and (2).
Trvalý link: http://hdl.handle.net/11104/0268530