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dc.contributor.authorAghajani, Asadollah ( Orcid Icon 0000-0002-6656-113X )
dc.contributor.authorMosleh Tehrani, Alireza ( )
dc.date.accessioned2022-03-28T17:43:57Z
dc.date.available2022-03-28T17:43:57Z
dc.date.issued2017-02-14
dc.identifier.citationAghajani, A., & Mosleh Tehrani, A. (2017). Pointwise bounds for positive supersolutions of nonlinear elliptic problems involving the p-Laplacian. Electronic Journal of Differential Equations, 2017(46), pp. 1-14.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/15570
dc.description.abstractWe derive a priori bounds for positive supersolutions of -∆pu = ρ(x)ƒ(u), where p > 1 and ∆p is the p-Laplace operator, in a smooth bounded domain of ℝN with zero Dirichlet boundary conditions. We apply our results to the nonlinear elliptic eigenvalue problem -∆pu = λƒ(u), with Dirichlet boundary condition, where ƒ is a nondecreasing continuous differentiable function on such that ƒ(0) > 0, ƒ(t)1/(p-1) is superlinear at infinity, and give sharp upper and lower bounds for the extremal parameter λ*p. In particular, we consider the nonlinearities ƒ(u) = eu and ƒ(u) = (1 + u)m (m > p - 1) and give explicit estimates on λ*p. As a by-product of our results, we obtain a lower bound for the principal eigenvalue of the p-Laplacian that improves obtained results in the recent literature for some range of p and N.
dc.formatText
dc.format.extent14 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2017, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectNonlinear eigenvalue problemen_US
dc.subjectEstimates of principal eigenvalueen_US
dc.subjectExtremal parameteren_US
dc.titlePointwise bounds for positive supersolutions of nonlinear elliptic problems involving the p-Laplacianen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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