SPIKE-LAYERED SOLUTIONS OF SINGULARLY PERTURBED QUASILINEAR DIRICHLET PROBLEMS ON BALL

• 来源期刊: 偏微分方程（英文版）
• 学科: 数学
• 关键词: Quasilinear Dirichlet problem peak point unique.
• 年，卷（期）: 2002,（4）
• 页码范围: 65-80
• 页数: 16页
• 分类号: O175.25.
• 语种: 英文

摘要

We consider the singularly perturbed quasilinear Dirichlet problems of the form -∈Δpu = f(u) in Ω u≥0 in Ω, u=0 on Ω where Δpu = div(|Du|p-2Du),p ＞ 1,f is subcritical, ∈＞ 0 is a small parameter and Ω is a bounded smooth domain in RN (N ≥2). When Ω = B1 = {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.