TY - JOUR
T1 - Spike-layered Solutions of Singularly Perturbed Quasilinear Dirichlet Problems on Ball
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.