Abstract
This paper mainly investigates the extrema of a nonconvex functional with double-well potential in 1D through the approach of nonlinear differential equations. Based on the canonical duality method, the corresponding Euler–Lagrange equation with Neumann boundary condition can be converted into a cubic dual algebraic equation, which will help find the local extrema for the primal problem.
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Dedicated to Professor Jim Hill on the occasion of his 70th birthday.
This article is part of the topical collection “James Hill” guest edited by Scott McCue and Natalie Thamwattana.
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Gao, D.Y., Lu, X. On the extrema of a nonconvex functional with double-well potential in 1D. Z. Angew. Math. Phys. 67, 62 (2016). https://doi.org/10.1007/s00033-016-0636-0
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DOI: https://doi.org/10.1007/s00033-016-0636-0