Periodic forcing of solutions of a boundary value problem for a second-order differential equation in Hilbert space |
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Authors: | Ronald E Bruck |
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Institution: | Department of Mathematics, University of Southern California, Los Angeles, California 90007 USA |
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Abstract: | We show that if u is a bounded solution on + of u″(t) ?Au(t) + f(t), where A is a maximal monotone operator on a real Hilbert space H and f∈Lloc2(+;H) is periodic, then there exists a periodic solution ω of the differential equation such that u(t) ? ω(t) 0 and u′(t) ? ω′(t) → 0 as t → ∞. We also show that the two-point boundary value problem for this equation has a unique solution for boundary values in and that a smoothing effect takes place. |
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