A Nonlinear Beam Equation Arising in the Theory of Elastic Bodies

Abstract

We study the global solvability of a nonlinear Cauchy problem, which arises in the theory of oscillations in elastic bodies. We show that the linearized problem defines a contraction semigroup, which is then used to transform the Cauchy problem into an integral equation. Finally, it is shown that the corresponding integral operator has a unique fixed point, which gives rise to a global solution of the original nonlinear problem.