Summary
This paper deals with a nonlinear eigenvalue problem of variational type which describes the everted equilibrium shapes of a thin elastic spherical cap. The everted solutions of the equilibrium problem do exist under certain conditions involving the relative magnitudes of the geometrical parameters characterizing the cap. In the mathematical formulation the everted solution and the significant parameters respectively correspond to the nontrivial zeros and the eigenvalues of a nonlinear completely continuous operator. The present paper characterizes the spectrum as well as the correspondent path of solutions.
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Rosati, M. A nonlinear eigenvalue problem governing the eversion of elastic spherical caps. Annali di Matematica pura ed applicata 159, 189–210 (1991). https://doi.org/10.1007/BF01766301
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DOI: https://doi.org/10.1007/BF01766301