Somayeh Khademloo

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1 1 , , 0, , r s p u u h x u dx g x u dx x u x + + −∆ = + ∈ Ω = ∈ ∂Ω () 1, 0 p W Ω () () () 1 1 , 0. r s p u x h x u dx g x u dx in u on + +  −∆ = + Ω   = ∂Ω   () E () () 1 1 / r p s Np N p N p < < − < < − + − () () () 0 0 r h L L C ∞ ∈ Ω Ω Ω   0 1 1 1, r r p * + + = ()() 0. 1 Np r Np r N p = − + − () () 0 s g L L ∞ ∈ Ω Ω  0 1 1 1, s s p * + + =(More)
We study the following quasilinear problem with nonlinear boundary condition −Δpu − λa x u|u|p−2 b x u|u|γ−2, in Ω and 1 − α |∇u|p−2 ∂u/∂n αu|u|p−2 0, on ∂Ω, where Ω ⊆ R is a connected bounded domain with smooth boundary ∂Ω, the outward unit normal to which is denoted by n.Δp is the p-Laplcian operator defined byΔpu div |∇u|p−2∇u , the functions a and b are(More)
where ⊂RN (N ≥ ) is a smooth bounded domain such that ξi ∈ , i = , , . . . ,k, k ≥ , are different points, ≤ μi < μ̄ := (N–  ), L := – · – ∑k i=μi · |x–ξi| , η,λ,σ ≥ , a,a,a ∈ R,  < α, β < ∗ – , α + β = ∗. We work in the product space H ×H , where the space H :=H ( ) is the completion of C∞  ( ) with respect to the norm ( ∫ |∇ · | dx)(More)
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