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dc.contributor.authorKaratson, Janos ( )
dc.contributor.authorSimon, Peter L ( Orcid Icon 0000-0002-2183-1853 )
dc.date.accessioned2019-11-21T20:55:05Z
dc.date.available2019-11-21T20:55:05Z
dc.date.issued1999-10-18
dc.identifier.citationKaratson, J., & Simon, P. L. (1999). Bifurcations for semilinear elliptic equations with convex nonlinearity. Electronic Journal of Differential Equations, 1999(43), pp. 1-16.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/8863
dc.description.abstractWe investigate the exact number of positive solutions of the semilinear Dirichlet boundary value problem Δu + f(u) = 0 on a ball in Rn where f is a strictly convex C2 function on [0,∞). For the one-dimensional case we classify all strictly convex C2 functions according to the shape of the bifurcation diagram. The exact number of positive solutions may be 2, 1, or 0, depending on the radius. This full classification is due to our main lemma, which implies that the time-map cannot have a minimum. For the case n>1 we prove that for sublinear functions there exists a unique solution for all R. For other convex functions estimates are given for the number of positive solutions depending on R. The proof of our results relies on the characterization of the shape of the time-map.en_US
dc.formatText
dc.format.extent16 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, 1999, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectSemilinear elliptic equationsen_US
dc.subjectTime-mapen_US
dc.subjectBifurcation diagramen_US
dc.titleBifurcations for Semilinear Elliptic Equations with Convex Nonlinearityen_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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