A nonlinear beam equation Original Research Article

The existence and uniqueness of weak solutions to a nonlinear beam equation are established under relaxed assumptions (locally Lipschitz plus affine domination) on the nonlinearity in the stiffness constitutive law. The results provide alternatives to previous theories requiring rather stringent monotonicity assumptions. The techniques and arguments are applicable to a large class of nonlinear second-order (in time) partial differential equation systems.