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Periodic solutions of semilinear wave equations with discontinuous nonlinearities (2015)

In-Sook Kim; Jung-Hyun Bae; Suk-Joon Hong

Springer

In: Boundary Value Problems

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Publication Date: 2015-10-30

Description: We study the periodic Dirichlet problem for a semilinear wave equation with discontinuous nonlinearity. First we establish a continuation theorem for a semilinear operator equation in a Hilbert space, where a key tool is the Berkovits-Tienari degree theory for a class of perturbations of monotone type of a densely defined closed linear operator. Applying the continuation theorem, we prove the main results on the solvability of the given semilinear wave equation, with the aid of spectral theory for densely defined closed linear operators.MSC: 35L05, 35R05, 47H04, 47H05, 47H11.

Print ISSN: 1687-2762

Electronic ISSN: 1687-2770

Topics: Mathematics

Published by Springer

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