An averaging method for singularly perturbed systems of semilinear differential inclusions with analytic semigroups
✍ Scribed by Mikhail Kamenskii; Paolo Nistri
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 159 KB
- Volume
- 53
- Category
- Article
- ISSN
- 0362-546X
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✦ Synopsis
We consider a system of two semilinear parabolic inclusions depending on a small parameter ¿ 0 which is present both in front of the derivative in one of the two inclusions and in the nonlinear terms to model high-frequency inputs.
The aim is to provide conditions in order to guarantee, for ¿ 0 su ciently small, the existence of periodic solutions and in order to study their behaviour as tends to zero. Our assumptions permit the deÿnition of upper semicontinuous, convex valued, compact vector operators whose ÿxed points represent the sought-after periodic solutions. The existence of ÿxed points is shown by using topological degree theory arguments.