The solution existence and convergence analysis for linear and nonlinear differential-operator equations in Banach spaces within the Calogero type projection-algebraic scheme of discrete approximations

Miroslaw Lustyk 1 , Julian Janus 1 , Marzenna Pytel-Kudela 1 ,  and Anatoliy Prykarpatsky
  • 1 The AGH University of Science and Technology, Krakow, Poland
  • 2 The Abdus Salam International Center of Theoretical Physics, Trieste, Italy
  • 3 Ivan Franko State Pedagogical University, Drohobych, Lviv region, Ukraine


The projection-algebraic approach of the Calogero type for discrete approximations of linear and nonlinear differential operator equations in Banach spaces is studied. The solution convergence and realizability properties of the related approximating schemes are analyzed. For the limiting-dense approximating scheme of linear differential operator equations a new convergence theorem is stated. In the case of nonlinear differential operator equations the effective convergence conditions for the approximated solution sets, based on a Leray-Schauder type fixed point theorem, are obtained.

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