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dc.contributor.authorQian, Xiaotao ( Orcid Icon 0000-0001-7470-4340 )
dc.contributor.authorChen, Jianqing ( Orcid Icon 0000-0002-5998-7802 )
dc.date.accessioned2022-02-16T20:08:18Z
dc.date.available2022-02-16T20:08:18Z
dc.date.issued2018-07-17
dc.identifier.citationQian, X., & Chen, J. (2018). Existence of multiple solutions and estimates of extremal values for a Kirchhoff type problem with fast increasing weight and critical nonlinearity. Electronic Journal of Differential Equations, 2018(144), pp. 1-19.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/15344
dc.description.abstract

In this article, we study the Kirchhoff type problem

-(α + ε ∫3 K(x)|∇u|2dx) div(K(x)∇u) = λK(x)ƒ(x)|u|q-2u + K(x)|u|4u,

where x ∈ ℝ3, 1 < q < 2, K(x) = exp(|x|α/4) with α ≥ 2, ε > 0 is small enough, and the parameters α, λ > 0. Under some assumptions on ƒ(x), we establish the existence of two nonnegative nontrivial solutions and obtain uniform lower estimates for extremal values of the problem via variational methods.

dc.formatText
dc.format.extent19 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2018, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectVariational methodsen_US
dc.subjectKirchhoff type equationen_US
dc.subjectCritical nonlinearityen_US
dc.subjectMultiple solutionsen_US
dc.subjectExtremal valuesen_US
dc.titleExistence of multiple solutions and estimates of extremal values for a Kirchhoff type problem with fast increasing weight and critical nonlinearityen_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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