An approximation solvability method for nonlocal semilinear differential problems in Banach spaces

Irene Benedetti; Nguyen Van Loi; Valentina Taddei

doi:10.3934/dcds.2017128

Article Contents

2017, Volume 37, Issue 6: 2977-2998. Doi: 10.3934/dcds.2017128

This issue Previous Article Li-Yorke chaos for dendrite maps with zero topological entropy and ω-limit sets Next Article Scattering of solutions to the nonlinear Schrödinger equations with regular potentials

An approximation solvability method for nonlocal semilinear differential problems in Banach spaces

1.
Department of Mathematics and Computer Sciences, University of Perugia, Italy
2.
Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh city, Viet Nam
3.
Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh city, Viet Nam
4.
Department of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia, Italy

* Corresponding author: Nguyen Van Loi
* Corresponding author: Nguyen Van Loi

Received: August 31, 2016

Revised: December 31, 2016

Published: May 2017

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Abstract

A new approximation solvability method is developed for the study of semilinear differential equations with nonlocal conditions without the compactness of the semigroup and of the nonlinearity. The method is based on the Yosida approximations of the generator of C₀-semigroup, the continuation principle, and the weak topology. It is shown how the abstract result can be applied to study the reaction-diffusion models.

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Mathematics Subject Classification: Primary: 35R09; Secondary: 34B10, 34C25, 47H11.

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References

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