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On the existence of canard solutions

Daniel Panazzolo (2000)

Publicacions Matemàtiques

We study the existence of global canard surfaces for a wide class of real singular perturbation problems. These surfaces define families of solutions which remain near the slow curve as the singular parameter goes to zero.

Structure of stable solutions of a one-dimensional variational problem

Nung Kwan Yip (2006)

ESAIM: Control, Optimisation and Calculus of Variations

We prove the periodicity of all H2-local minimizers with low energy for a one-dimensional higher order variational problem. The results extend and complement an earlier work of Stefan Müller which concerns the structure of global minimizer. The energy functional studied in this work is motivated by the investigation of coherent solid phase transformations and the competition between the effects from regularization and formation of small scale structures. With a special choice of a bilinear double...

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