Positive solution for a quasilinear equation with critical growth in $ℝ^N$

Lin Chen; Caisheng Chen; Zonghu Xiu

Positive solution for a quasilinear equation with critical growth in

ℝ^{N}

Lin Chen ; Caisheng Chen ; Zonghu Xiu

Annales Polonici Mathematici, Tome 116 (2016), p. 251-262 / Harvested from The Polish Digital Mathematics Library

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Résumé

We study the existence of positive solutions of the quasilinear problem ⎧ $- Δ_{N} u + {V (x) | u |}^{N - 2} u = {f (u, | \nabla u |}^{N - 2} \nabla u)$ , $x \in ℝ^{N}$ , ⎨ ⎩ u(x) > 0, $x \in ℝ^{N}$ , where $Δ_{N} u = {d i v (| \nabla u |}^{N - 2} \nabla u)$ is the N-Laplacian operator, $V : ℝ^{N} \to ℝ$ is a continuous potential, $f : ℝ \times ℝ^{N} \to ℝ$ is a continuous function. The main result follows from an iterative method based on Mountain Pass techniques.

Publié le : 2016-01-01

Zbl 06586886

EUDML-ID : urn:eudml:doc:280577

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     author = {Lin Chen and Caisheng Chen and Zonghu Xiu},
     title = {Positive solution for a quasilinear equation with critical growth in $$\mathbb{R}$^N$
            },
     journal = {Annales Polonici Mathematici},
     volume = {116},
     year = {2016},
     pages = {251-262},
     zbl = {06586886},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap3664-1-2016}
}

Lin Chen; Caisheng Chen; Zonghu Xiu. Positive solution for a quasilinear equation with critical growth in $ℝ^N$
            . Annales Polonici Mathematici, Tome 116 (2016) pp. 251-262. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap3664-1-2016/