A nonlinear eigenvalue problem governing the eversion of elastic spherical caps
A nonlinear eigenvalue problem for a system of two ordinary differential equations describing the statical equilibrium of a thin elastic spherical cap is treated using the variational formulation. The everted equilibrium shapes of the spherical cap exist under certain conditions involving the relative magnitudes of the geometrical parameters characterizing the cap. The non-trivial solutions of the studied nonlinear eigenvalue problem can be obtained as extremals of certain functional. A refined form of the steepest descent method is applied to follow the complete path of the solution. The characterization of the spectrum and the correspondent path of the solutions are given with the help of an extension technique.
scientific article; zbMATH DE number 59773
scientific article