Existence of solutions for Kirchhoff type equations with unbounded potential

dc.contributor.authorDuan, Yueliang
dc.contributor.authorZhou, Yinggao
dc.date.accessioned2022-06-08T19:42:34Z
dc.date.available2022-06-08T19:42:34Z
dc.date.issued2017-07-19
dc.description.abstractIn this article, we study the Kirchhoff type equation (α + λ ∫ℝ3 |∇u|2 + λb ∫ℝ3u2) [-∆u + bu] = K(x)|u|p-1u, in ℝ3, where α, b > 0, p ∈ (2, 5), λ ≥ 0 is a parameter, and K may be an unbounded potential function. By using variational methods, we prove the existence of nontrivial solutions for the above equation. A cut-off functional and some estimates are used to obtain the bounded Palais-Smale sequences.
dc.description.departmentMathematics
dc.formatText
dc.format.extent12 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationDuan, Y., & Zhou, Y. (2017). Existence of solutions for Kirchhoff type equations with unbounded potential. <i>Electronic Journal of Differential Equations, 2017</i>(184), pp. 1-12.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/15877
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.holderThis work is licensed under a Creative Commons Attribution 4.0 International License.
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2017, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectCut-off functional
dc.subjectKirchhoff type problem
dc.subjectUnbounded potential
dc.subjectVariational method
dc.titleExistence of solutions for Kirchhoff type equations with unbounded potential
dc.typeArticle

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