Opuscula Math. 34, no. 2 (2014), 327-338
http://dx.doi.org/10.7494/OpMath.2014.34.2.327

 
Opuscula Mathematica

Global convergence of successive approximations of the Darboux problem for partial functional differential equations with infinite delay

Tomasz Człapiński

Abstract. We consider the Darboux problem for the hyperbolic partial functional differential equation with infinite delay. We deal with generalized (in the "almost everywhere" sense) solutions of this problem. We prove a theorem on the global convergence of successive approximations to a unique solution of the Darboux problem.

Keywords: successive approximations, Darboux problem, infinite delay.

Mathematics Subject Classification: 35R10.

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  • Tomasz Człapiński
  • University of Gdansk, Institute of Mathematics, Wita Stwosza 57, 80-952 Gdansk, Poland
  • Received: 2012-10-25.
  • Revised: 2014-02-09.
  • Accepted: 2014-02-21.
Opuscula Mathematica - cover

Cite this article as:
Tomasz Człapiński, Global convergence of successive approximations of the Darboux problem for partial functional differential equations with infinite delay, Opuscula Math. 34, no. 2 (2014), 327-338, http://dx.doi.org/10.7494/OpMath.2014.34.2.327

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