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dc.contributor.authorChmaj, Adam J. J. ( )
dc.contributor.authorRen, Xiaofeng ( )
dc.date.accessioned2020-07-07T19:25:16Z
dc.date.available2020-07-07T19:25:16Z
dc.date.issued2002-01-02
dc.identifier.citationChmaj, A. J. J., & Ren, X. (2002). The nonlocal bistable equation: Stationary solutions on a bounded interval. Electronic Journal of Differential Equations, 2002(02), pp. 1-12.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/11980
dc.description.abstractWe 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 C1 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.en_US
dc.formatText
dc.format.extent12 pages
dc.format.medium1 file (.pdf)
dc.language.isoen_USen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2002, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectLocal minimizersen_US
dc.subjectMonotone solutionsen_US
dc.titleThe Nonlocal Bistable Equation: Stationary Solutions on a Bounded Intervalen_US
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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