We consider the singularly perturbed quasilinear Dirichlet problems of the form {-εΔpu=f(u) in Ω，u≥0 in Ω，u=0 on δΩ where Δpu=div(|Du)^p-2Du),p>1,f is subcritical,ε>0 is a small parameter and Ω is a...We consider the singularly perturbed quasilinear Dirichlet problems of the form {-εΔpu=f(u) in Ω，u≥0 in Ω，u=0 on δΩ where Δpu=div(|Du)^p-2Du),p>1,f is subcritical,ε>0 is a small parameter and Ω is a bounded smooth domain in R^N(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 ε→0.展开更多
文摘We consider the singularly perturbed quasilinear Dirichlet problems of the form {-εΔpu=f(u) in Ω，u≥0 in Ω，u=0 on δΩ where Δpu=div(|Du)^p-2Du),p>1,f is subcritical,ε>0 is a small parameter and Ω is a bounded smooth domain in R^N(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 ε→0.
