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A generalized Cauchy problem for hyperbolic functional differential systems is considered. The initial problem is transformed into a system of functional integral equations. The existence of solutions of this system is proved by using the method of successive approximations. Differentiability of solutions with respect to initial functions is proved. It is important that functional differential systems considered in this paper do not satisfy the Volterra condition.
Elżbieta Puźniakowska-Gałuch. "Generalized Cauchy problems for hyperbolic functional differential systems." Annales Polonici Mathematici 110.1 (2014): 33-53. <http://eudml.org/doc/280266>.
@article{ElżbietaPuźniakowska2014, abstract = {A generalized Cauchy problem for hyperbolic functional differential systems is considered. The initial problem is transformed into a system of functional integral equations. The existence of solutions of this system is proved by using the method of successive approximations. Differentiability of solutions with respect to initial functions is proved. It is important that functional differential systems considered in this paper do not satisfy the Volterra condition.}, author = {Elżbieta Puźniakowska-Gałuch}, journal = {Annales Polonici Mathematici}, keywords = {hyperbolic functional differential systems; generalized Cauchy problems; functional integral equations; method of successive approximations}, language = {eng}, number = {1}, pages = {33-53}, title = {Generalized Cauchy problems for hyperbolic functional differential systems}, url = {http://eudml.org/doc/280266}, volume = {110}, year = {2014}, }
TY - JOUR AU - Elżbieta Puźniakowska-Gałuch TI - Generalized Cauchy problems for hyperbolic functional differential systems JO - Annales Polonici Mathematici PY - 2014 VL - 110 IS - 1 SP - 33 EP - 53 AB - A generalized Cauchy problem for hyperbolic functional differential systems is considered. The initial problem is transformed into a system of functional integral equations. The existence of solutions of this system is proved by using the method of successive approximations. Differentiability of solutions with respect to initial functions is proved. It is important that functional differential systems considered in this paper do not satisfy the Volterra condition. LA - eng KW - hyperbolic functional differential systems; generalized Cauchy problems; functional integral equations; method of successive approximations UR - http://eudml.org/doc/280266 ER -