caa a22 4500 378878557 CHVBK 20180305123426.0 cr unu---uuuuu 161128e200309 xx s 000 0 eng 10.1515/GMJ.2003.509 doi (NATIONALLICENCE)gruyter-10.1515/GMJ.2003.509 First Order Partial Functional Differential Equations with Unbounded Delay [Elektronische Daten] [Z. Kamont, S. Kozieł] The phase space for nonlinear hyperbolic functional differential equations with unbounded delay is constructed. The set of axioms for generalized solutions of initial problems is presented. A theorem on the existence and continuous dependence upon initial data is given. The Cauchy problem is transformed into a system of integral functional equations. The existence of solutions of this system is proved by the method of successive approximations and by using theorems on integral inequalities. Examples of phase spaces are given. © Heldermann Verlag unbounded delay nationallicence bicharacteristics nationallicence local existence nationallicence generalized solutions nationallicence Kamont Z. Institute of Mathematics, University of Gdańsk, Wit Stwosz Street 57, 80-952 Gdańsk, Poland. E-mail: zkamont@math.univ.gda.pl aut Kozieł S. Institute of Mathematics, University of Gdańsk, Wit Stwosz Street 57, 80-952 Gdańsk, Poland aut Georgian Mathematical Journal Walter de Gruyter GmbH & Co. KG 10/3(2003-09), 509-530 1072-947X 10:3<509 2003 10 GMJ https://doi.org/10.1515/GMJ.2003.509 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/GMJ.2003.509 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kamont Z. Institute of Mathematics, University of Gdańsk, Wit Stwosz Street 57, 80-952 Gdańsk, Poland. E-mail: zkamont@math.univ.gda.pl aut NATIONALLICENCE 700 1- Kozieł S. Institute of Mathematics, University of Gdańsk, Wit Stwosz Street 57, 80-952 Gdańsk, Poland aut NATIONALLICENCE 773 0- Georgian Mathematical Journal Walter de Gruyter GmbH & Co. KG 10/3(2003-09), 509-530 1072-947X 10:3<509 2003 10 GMJ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter