Systems of coupled clamped beams equations with full nonlinear terms: Existence and location results. (June 2017) - Minhós, Feliz; Coxe, Infeliz
Abstract: This work gives sufficient conditions for the solvability of the fourth order coupled system u ( 4 ) ( t ) = f ( t, u ( t ), u ′ ( t ), u ″ ( t ), u ‴ ( t ), v ( t ), v ′ ( t ), v ″ ( t ), v ‴ ( t ) ) v ( 4 ) ( t ) = h ( t, u ( t ), u ′ ( t ), u ″ ( t ), u ‴ ( t ), v ( t ), v ′ ( t ), v ″ ( t ), v ‴ ( t ) ) with f, h : [ 0, 1 ] × R 8 → R some L 1 - Carathéodory functions, and the boundary conditions u ( 0 ) = u ′ ( 0 ) = u ″ ( 0 ) = u ″ ( 1 ) = 0 v ( 0 ) = v ′ ( 0 ) = v ″ ( 0 ) = v ″ ( 1 ) = 0 . To the best of our knowledge, it is the first time in the literature where two beam equations are considered with full nonlinearities, that is, with dependence on all derivatives of u and v . An application to the study of the bending of two elastic coupled clamped beams is considered.,