Existence and non-existence of solutions for Timoshenko-type equations with variable exponents

Antontsev, Stanislav N.Ferreira, JorgePiskin, ErhanSiqueira Cordeiro, Sebastiao Martins2024-04-242024-04-2420211468-12181878-5719https://doi.org/10.1016/j.nonrwa.2021.103341https://hdl.handle.net/11468/15915In 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.eninfo:eu-repo/semantics/closedAccessLocal ExistenceNonexistenceTimoshenko EquationVariable ExponentExistence and non-existence of solutions for Timoshenko-type equations with variable exponentsExistence and non-existence of solutions for Timoshenko-type equations with variable exponentsArticle61WOS:0006576148000092-s2.0-8510569183010.1016/j.nonrwa.2021.103341Q1Q1