文摘
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]×R8→Rf,h:[0,1]×R8→R some L1L1- Carathéodory functions, and the boundary conditions {u(0)=u′(0)=u″(0)=u″(1)=0v(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 uu and vv.An application to the study of the bending of two elastic coupled clamped beams is considered.