Geodesic
The nonlocal bistable equation: Stationary solutions on a bounded interval
Electronic Journal of Differential Equations, Tome 2002 (2002).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We discuss instability and existence issues for the nonlocal bistable equation. This model arises as the Euler-Lagrange equation of a nonlocal, van der Waals type functional. Taking the viewpoint of the calculus of variations, we prove that for a class of nonlocalities this functional does not admit nonconstant $C^{1}$ local minimizers. By taking variations along non-smooth paths, we give examples of nonlocalities for which the functional does not admit local minimizers having a finite number of discontinuities. We also construct monotone solutions and give a criterion for nonexistence of nonconstant solutions.
Classification : 45G10
Keywords: local minimizers, monotone solutions 
@article{EJDE_2002__2002__a147,
     author = {Chmaj, Adam J.J. and Ren, Xiaofeng},
     title = {The nonlocal bistable equation: {Stationary} solutions on a bounded interval},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2002},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a147/}
}
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Chmaj, Adam J.J.; Ren, Xiaofeng. The nonlocal bistable equation: Stationary solutions on a bounded interval. Electronic Journal of Differential Equations, Tome 2002 (2002). http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a147/