The nonlocal bistable equation: Stationary solutions on a bounded interval

Adam J J Chmaj, Xiaofeng Ren

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


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 local minimizers. By taking variations along nonsmooth 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. © 2002 Southwest Texas State University.

Original languageEnglish
Pages (from-to)XXXXI-XXXXII
JournalElectronic Journal of Differential Equations
Publication statusPublished - 2002


  • Local minimizers
  • Monotone solutions


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