Global Solutions of IBVP to Nonlinear Equation of Suspended String

Abstract

We shall consider IBVP to a nonlinear equation of suspended string with uniform density to which a nonlinear time-independent outer force works. We shall show the existence of time-global weak solutions of IBVP. To prove our result we shall use the function spaces defined by [Ya1], and apply the method due to Sattinger [Sat] based on the potential-well and the Galerkin method.