Existence of a positive ground state solution for a Kirchhoff type problem involving a critical exponent

Lan Zeng; Chun Lei Tang

Lan Zeng ; Chun Lei Tang

Annales Polonici Mathematici, Tome 116 (2016), p. 163-179 / Harvested from The Polish Digital Mathematics Library

Résumé

We consider the following Kirchhoff type problem involving a critical nonlinearity: ⎧ $- [a + b (\int_{Ω} {| \nabla u | ² d x)}^{m} {] Δ u = f (x, u) + | u |}^{2 * - 2} u$ in Ω, ⎨ ⎩ u = 0 on ∂Ω, where $Ω \subset ℝ^{N}$ (N ≥ 3) is a smooth bounded domain with smooth boundary ∂Ω, a > 0, b ≥ 0, and 0 < m < 2/(N-2). Under appropriate assumptions on f, we show the existence of a positive ground state solution via the variational method.

Publié le : 2016-01-01

Zbl 06622313

EUDML-ID : urn:eudml:doc:286189

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     author = {Lan Zeng and Chun Lei Tang},
     title = {Existence of a positive ground state solution for a Kirchhoff type problem involving a critical exponent},
     journal = {Annales Polonici Mathematici},
     volume = {116},
     year = {2016},
     pages = {163-179},
     zbl = {06622313},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap3783-1-2016}
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Lan Zeng; Chun Lei Tang. Existence of a positive ground state solution for a Kirchhoff type problem involving a critical exponent. Annales Polonici Mathematici, Tome 116 (2016) pp. 163-179. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap3783-1-2016/