Opuscula Math. 35, no. 6 (2015), 915-933
http://dx.doi.org/10.7494/OpMath.2015.35.6.915
Opuscula Mathematica
On the quasilinear Cauchy problem for a hyperbolic functional differential equation
Abstract. The Cauchy problem for hyperbolic functional differential equations is considered. Volterra and Fredholm dependence are considered. A theorem on the local existence of generalized solutions defined on the Haar pyramid is proved. A result on differentiability of a solution with respect to initial data is proved.
Keywords: functional differential equations, Haar pyramid, differentiability of solutions, Fredholm type of equation.
Mathematics Subject Classification: 35R10, 35F25, 35A05.
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- Elżbieta Puźniakowska-Gałuch
- University of Gdańsk, Institute of Mathematics, Wit Stwosz Street 57, 80-952 Gdańsk, Poland
- Communicated by Mirosław Lachowicz.
- Received: 2014-08-17.
- Revised: 2014-11-03.
- Accepted: 2014-11-04.
- Published online: 2015-06-06.
