Hybrid delay evolution systems with nonlinear constraints


Motivated by the importance of reaction-diffusion systems in modeling real processes with memory, we are interested in the existence of mild solutions for systems of abstract delay evolution equations subjected to general nonlinear constraints. Wishing to allow the system nonlinearities to behave independently as much as possible, we use a vector approach based on matrices, vector-valued norms and a vector version of Krasnoselskii’s fixed point theorem for a sum of two operators. The hybrid character of the systems comes from the different nature of the metrical and topological conditions imposed to the component equations. Also, the assumptions are put in connection with the support of the nonlinear constraints. Two examples are given to illustrate the theory.


Octavia-Maria Bolojan
Department of Mathematics, Babes–Bolyai University,  Cluj-Napoca, Romania

Radu Precup
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania


nonlinear evolution equation; nonlocal initial condition; delay; Krasnoselskii’s fixed point theorem for a sum of operators

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O.-M. Bolojan, R. Precup, Hybrid delay evolution systems with nonlinear constraints, Dynamic Systems and Applications, 27 (2018) no. 4, 773-790, http://doi.org/10.12732/dsa.v27i4.6


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Dynamic Systems and Applications

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Dynamic Publishers, Inc., Acad. Publishers, Ltd.

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