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    Existence and non-existence of solutions for Timoshenko-type equations with variable exponents
    (Pergamon-Elsevier Science Ltd, 2021) Antontsev, Stanislav N.; Ferreira, Jorge; Piskin, Erhan; Siqueira Cordeiro, Sebastiao Martins
    In this work, we investigate the following nonlinear Timoshenko variable exponents: u(tt) + Delta(2)u - M (parallel to del u parallel to(2)(L2(Omega))) Delta u + vertical bar u(t)vertical bar(p(x)-2) u(t) = vertical bar u vertical bar(q(x)-2)u. By using the Faedo-Galerkin method, we prove the local existence of the solution under suitable conditions. We also investigate the nonexistence of solutions with negative initial energy. Published by Elsevier Ltd.