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An approximation solvability method for Nonlocal semilinear differential problems in banach spaces


Irene Benedetti, Nguyen Van Loi* and Valentina Taddei

Source title: 
Discrete and Continuous Dynamical Systems, 37(6): 2977-2998, 2017 (ISI)
Academic year of acceptance: 

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.