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Mountain pass solutions for a double-well energy
journal contribution
posted on 2023-06-07, 19:28 authored by Kewei ZhangWe establish the existence of a mountain pass solution for a variational integral involving a quasiconvex function with a double-well structure in the geometrically linear elasticity setting. We show that under small dead-load perturbations, the Neumann boundary value problem has at least three solutions, a global minimizer, a local minimizer and a mountain pass solution. We show that our variational integral satisfies a Weak Palais–Smale condition (WPS) hence the mountain pass lemma applies.
History
Publication status
- Published
Journal
Journal of Differential EquationsISSN
0022-0396Publisher
ElsevierExternal DOI
Issue
2Volume
182Page range
490-510Pages
20.0Department affiliated with
- Mathematics Publications
Full text available
- No
Peer reviewed?
- Yes