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Periodic solutions of time-dependent, semilinear evolution equations of compact type
Published online by Cambridge University Press: 14 November 2011
Synopsis
We establish the existence of solutions in a weak sense of
where t Є J = [0, T] and′ = d/dt. It is supposed that the unbounded, linear operators A(t) generate analytic and compact semigroups on a Hilbert space H and that B(t, x) are bounded linear operators. The function f(t, x) with values in H may have asymptotically sublinear growth.
We prove the existence of a periodic solution with the help of Schauder’s fixed point theorem.
Accordingly, we first verify that the corresponding linearized version of (0.1),
has a unique solution for each square integrable ψ(t), provided that the homogeneous problem has only the zero solution.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 95 , Issue 1-2 , 1983 , pp. 7 - 24
- Copyright
- Copyright © Royal Society of Edinburgh 1983
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