Multiplicity results for a class of concave-convex elliptic systems involving sign-changing weight functions

Honghui Yin; Zuodong Yang

Annales Polonici Mathematici, Tome 101 (2011), p. 51-71 / Harvested from The Polish Digital Mathematics Library

Résumé

Our main purpose is to establish the existence of weak solutions of second order quasilinear elliptic systems ⎧ $- Δ_{p} u + {| u |}^{p - 2} u = f_{1 λ ₁} {(x) | u |}^{q - 2} u + 2 α / (α + β) g_{μ} {| u |}^{α - 2} u {| v |}^{β}$ , x ∈ Ω, ⎨ $- Δ_{p} v + {| v |}^{p - 2} v = f_{2 λ ₂} {(x) | v |}^{q - 2} v + 2 β / (α + β) g_{μ} {| u |}^{α} {| v |}^{β - 2} v$ , x ∈ Ω, ⎩ u = v = 0, x∈ ∂Ω, where 1 < q < p < N and $Ω \subset ℝ^{N}$ is an open bounded smooth domain. Here λ₁, λ₂, μ ≥ 0 and $f_{i λ_{i}} (x) = λ_{i} f_{i +} (x) + f_{i -} (x)$ (i = 1,2) are sign-changing functions, where $f_{i \pm} (x) = m a x \pm f_{i} (x), 0$ , $g_{μ} (x) = a (x) + μ b (x)$ , and $Δ_{p} u = {d i v (| \nabla u |}^{p - 2} \nabla u)$ denotes the p-Laplace operator. We use variational methods.

Publié le : 2011-01-01

Zbl 1229.35066

EUDML-ID : urn:eudml:doc:280861

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     author = {Honghui Yin and Zuodong Yang},
     title = {Multiplicity results for a class of concave-convex elliptic systems involving sign-changing weight functions},
     journal = {Annales Polonici Mathematici},
     volume = {101},
     year = {2011},
     pages = {51-71},
     zbl = {1229.35066},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap102-1-5}
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Honghui Yin; Zuodong Yang. Multiplicity results for a class of concave-convex elliptic systems involving sign-changing weight functions. Annales Polonici Mathematici, Tome 101 (2011) pp. 51-71. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap102-1-5/