We consider a system of two semilinear parabolic inclusions depending on a small parameter epsilon > 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 epsilon > 0 sufficiently small, the existence of periodic solutions and in order to study their behaviour as F tends to zero. Our assumptions permit the definition of upper semicontinuous, convex valued, compact vector operators whose fixed points represent the sought-after periodic solutions. The existence of fixed points is shown by using topological degree theory arguments. (C) 2003 Elsevier Science Ltd. All rights reserved.
M., K., Nistri, P. (2003). An averaging method for singularly perturbed systems of semilinear differential inclusions with analytic semigroups. NONLINEAR ANALYSIS, 53(3-4), 467-480 [10.1016/S0362-546X(02)00312-7].
An averaging method for singularly perturbed systems of semilinear differential inclusions with analytic semigroups
NISTRI, PAOLO
2003-01-01
Abstract
We consider a system of two semilinear parabolic inclusions depending on a small parameter epsilon > 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 epsilon > 0 sufficiently small, the existence of periodic solutions and in order to study their behaviour as F tends to zero. Our assumptions permit the definition of upper semicontinuous, convex valued, compact vector operators whose fixed points represent the sought-after periodic solutions. The existence of fixed points is shown by using topological degree theory arguments. (C) 2003 Elsevier Science Ltd. All rights reserved.File | Dimensione | Formato | |
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https://hdl.handle.net/11365/7186
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