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dc.contributor.authorMcGough, Jeff ( )
dc.contributor.authorMortensen, Jeff ( )
dc.contributor.authorRickett, Chris ( )
dc.contributor.authorStubbendieck, Gregg ( )
dc.date.accessioned2021-05-20T18:55:16Z
dc.date.available2021-05-20T18:55:16Z
dc.date.issued2005-03-22
dc.identifier.citationMcGough, J., Mortensen, J., Rickett, C., & Stubbendieck, G. (2005). Domain geometry and the Pohozaev identity. Electronic Journal of Differential Equations, 2005(32), pp. 1-16.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/13606
dc.description.abstractIn this paper, we investigate the boundary between existence and nonexistence for positive solutions of Dirichlet problem Δu + ƒ(u) = 0, where ƒ has supercritical growth. Pohozaev showed that for convex or polar domains, no positive solutions may be found. Ding and others showed that for domains with non-trivial topology, there are examples of existence of positive solutions. The goal of this paper is to illuminate the transition from non-existence to existence of solutions for the nonlinear eigenvalue problem as the domain moves from simple (convex) to complex (non-trivial topology). To this end, we present the construction of several domains in R3 which are not starlike (polar) but still admit a Pohozaev nonexistence argument for a general class of nonlinearities. One such domain is a long thin tubular domain which is curved and twisted in space. It presents complicated geometry, but simple topology. The construction (and the lemmas leading to it) are new and combined with established theorems narrow the gap between non-existence and existence strengthening the notion that trivial domain topology is the ingredient for non-existence.en_US
dc.formatText
dc.format.extent16 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University-San Marcos, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2005, San Marcos, Texas: Texas State University-San Marcos and University of North Texas.
dc.subjectPartial differential equationsen_US
dc.subjectVariational identitiesen_US
dc.subjectPohozaev identitiesen_US
dc.subjectNumerical methodsen_US
dc.titleDomain geometry and the Pohozaev identityen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
dc.description.departmentMathematics


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