Open AccessAn approximation solvability method for nonlocal semilinear differential problems in Banach spaces
Author(s) -
Irene Benedetti,
Nguyễn Văn Lợi,
Valentina Taddei
Publication year - 2017
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2017128
Subject(s) - semigroup , banach space , mathematics , compact space , continuation , generator (circuit theory) , analytic semigroup , nonlinear system , c0 semigroup , mathematical analysis , approximation property , pure mathematics , computer science , physics , power (physics) , quantum mechanics , programming language
A new approximation solvability method is developed for the study of semilinear dierential equations with nonlocal conditions without the compactness of the semigroup and of the nonlinearity. The method is based on\udthe Yosida approximations of the generator of C0semigroup, the continuation principle, and the weak topology. It is shown how the abstract result can be applied to study the reaction-diusion models