On a one- dimensional model of the finite elastostatics (Q1188381)

Summary: The deformation of a \(\text{rod }S=[0,1]\) is given by a diffeomorphism \(w: S\to S_ w=[0,w(1)]\) from the set \(\{w\in W^ 2_ 2(0,1): w(0)=0, w'(s)>0 (s\in S)\}\). The function \(\ln w'\) appears as measure of deformation. The function \(w\) is solution to a second order ordinary differential equation with the second boundary condition \(w'(1)=p\in\mathbb{R}^ +\). By an open-and-closed argument we show that the set of those \(p\) for which the boundary problem is uniquely solvable, is all \(\mathbb{R}^ +\).