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.
"Global Solutions of IBVP to Nonlinear Equation of Suspended String." Tokyo J. Math. 30 (2) 543 - 556, December 2007. https://doi.org/10.3836/tjm/1202136695