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dc.contributor.authorAlvarez-Caudevilla, Pablo ( Orcid Icon 0000-0003-1736-5818 )
dc.contributor.authorColorado, Eduardo ( Orcid Icon 0000-0002-1067-5752 )
dc.contributor.authorOrtega, Alejandro ( )
dc.date.accessioned2021-08-27T14:59:54Z
dc.date.available2021-08-27T14:59:54Z
dc.date.issued2021-06-14
dc.identifier.citationÁlvarez-Caudevilla, P., Colorado, E., & Ortega, A. (2021). Existence of positive solutions for Brezis-Nirenberg type problems involving an inverse operator. Electronic Journal of Differential Equations, 2021(52), pp. 1-24.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/14462
dc.description.abstractThis article concerns the existence of positive solutions for the second order equation involving a nonlocal term -Δu = γ(-Δ)-1 u + |u|p-1u, under Dirichlet boundary conditions. We prove the existence of positive solutions depending on the positive real parameter γ > 0, and up to the critical value of the exponent p, i.e. when 1 < p ≤ 2* - 1, where 2* = 2N/N-2 is the critical Sobolev exponent. For p = 2* - 1, this leads us to a Brezis-Nirenberg type problem, cf. [5], but, in our particular case, the linear term is a nonlocal term. The effect that this nonlocal term has on the equation changes the dimensions for which the classical technique based on the minimizers of the Sobolev constant, that ensures the existence of positive solution, going from dimensions N ≥ 4 in the classical Brezis-Nirenberg problem, to dimensions N ≥ 7 for this nonlocal problem.
dc.formatText
dc.format.extent24 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2021, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectCritical pointen_US
dc.subjectConcentration compactness principleen_US
dc.subjectMountain pass theoremen_US
dc.titleExistence of positive solutions for Brezis-Nirenberg type problems involving an inverse operatoren_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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