On Kirchhoff type problems involving critical and singular nonlinearities

Chun-Yu Lei; Chang-Mu Chu; Hong-Min Suo; Chun-Lei Tang

Chun-Yu Lei ; Chang-Mu Chu ; Hong-Min Suo ; Chun-Lei Tang

Annales Polonici Mathematici, Tome 113 (2015), p. 269-291 / Harvested from The Polish Digital Mathematics Library

Résumé

In this paper, we are interested in multiple positive solutions for the Kirchhoff type problem ⎧ $- (a + b \int_{Ω} | \nabla u | ² d x) Δ u = u ⁵ + λ u^{q - 1} / {| x |}^{β}$ in Ω ⎨ ⎩ u = 0 on ∂Ω, where Ω ⊂ ℝ³ is a smooth bounded domain, 0∈Ω, 1 < q < 2, λ is a positive parameter and β satisfies some inequalities. We obtain the existence of a positive ground state solution and multiple positive solutions via the Nehari manifold method.

Publié le : 2015-01-01

Zbl 1322.35153

EUDML-ID : urn:eudml:doc:280989

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     author = {Chun-Yu Lei and Chang-Mu Chu and Hong-Min Suo and Chun-Lei Tang},
     title = {On Kirchhoff type problems involving critical and singular nonlinearities},
     journal = {Annales Polonici Mathematici},
     volume = {113},
     year = {2015},
     pages = {269-291},
     zbl = {1322.35153},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap114-3-5}
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Chun-Yu Lei; Chang-Mu Chu; Hong-Min Suo; Chun-Lei Tang. On Kirchhoff type problems involving critical and singular nonlinearities. Annales Polonici Mathematici, Tome 113 (2015) pp. 269-291. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap114-3-5/