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Volume 15, Issue 4
Spike-layered Solutions of Singularly Perturbed Quasilinear Dirichlet Problems on Ball

Zhengce Zhang , Kaitai Li & Xiulan Guo

J. Part. Diff. Eq., 15 (2002), pp. 65-80.

Published online: 2002-11

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  • Abstract
We consider the singularly perturbed quasilinear Dirichlet problems of the form  {-∈Δ_pu = f(u) in Ω  u ≥ 0 in , u = 0 on ∂ Ω  where Δ_pu = div(|Du|^{p-2}Du), p > 1, f is subcritical. ∈ > 0 is a small parameter and  is a bounded smooth domain in R^N (N ≥ 2). When Ω = B_1 = {x; |x| < 1} is the unit ball, we show that the least energy solution is radially symmetric, the solution is also unique and has a unique peak point at origin as ∈ → 0.
  • Keywords

Quasilinear Dirichlet problem peak point unique

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@Article{JPDE-15-65, author = {Zhengce Zhang , Kaitai Li and Xiulan Guo }, title = {Spike-layered Solutions of Singularly Perturbed Quasilinear Dirichlet Problems on Ball}, journal = {Journal of Partial Differential Equations}, year = {2002}, volume = {15}, number = {4}, pages = {65--80}, abstract = { We consider the singularly perturbed quasilinear Dirichlet problems of the form  {-∈Δ_pu = f(u) in Ω  u ≥ 0 in , u = 0 on ∂ Ω  where Δ_pu = div(|Du|^{p-2}Du), p > 1, f is subcritical. ∈ > 0 is a small parameter and  is a bounded smooth domain in R^N (N ≥ 2). When Ω = B_1 = {x; |x| < 1} is the unit ball, we show that the least energy solution is radially symmetric, the solution is also unique and has a unique peak point at origin as ∈ → 0.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5462.html} }
TY - JOUR T1 - Spike-layered Solutions of Singularly Perturbed Quasilinear Dirichlet Problems on Ball AU - Zhengce Zhang , Kaitai Li & Xiulan Guo JO - Journal of Partial Differential Equations VL - 4 SP - 65 EP - 80 PY - 2002 DA - 2002/11 SN - 15 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5462.html KW - Quasilinear Dirichlet problem KW - peak point KW - unique AB - We consider the singularly perturbed quasilinear Dirichlet problems of the form  {-∈Δ_pu = f(u) in Ω  u ≥ 0 in , u = 0 on ∂ Ω  where Δ_pu = div(|Du|^{p-2}Du), p > 1, f is subcritical. ∈ > 0 is a small parameter and  is a bounded smooth domain in R^N (N ≥ 2). When Ω = B_1 = {x; |x| < 1} is the unit ball, we show that the least energy solution is radially symmetric, the solution is also unique and has a unique peak point at origin as ∈ → 0.
Zhengce Zhang , Kaitai Li and Xiulan Guo . (2002). Spike-layered Solutions of Singularly Perturbed Quasilinear Dirichlet Problems on Ball. Journal of Partial Differential Equations. 15 (4). 65-80. doi:
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