An approximation solvability method for nonlocal semilinear differential problems in Banach spaces. (English) Zbl 1357.35272
Summary: 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 \(C_0-\)semigroup, the continuation principle, and the weak topology. It is shown how the abstract result can be applied to study the reaction-diffusion models.
MSC:
| 35R09 | Integro-partial differential equations |
| 34B10 | Nonlocal and multipoint boundary value problems for ordinary differential equations |
| 34C25 | Periodic solutions to ordinary differential equations |
| 47H11 | Degree theory for nonlinear operators |
Keywords:
semilinear differential equation; nonlocal diffusion; approximation solvability method; nonlocal condition; degree theoryReferences:
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