Existence of regular and singular bound state solutions to a quasilinear equation - Wei-Chuan Wang (Boundary Value Problems)
Abstract The existence of regular and singular bound state solutions to △ p u + f ( u ) = 0 , r ∈ R n ∖ { 0 } $$ \triangle _{p}u+f(u)=0,~~~r\in \mathbb{R}^{n}\backslash \{0\} $$ is considered. Our result concerns the solution according to its behavior as r → 0 $r→ 0$ and r → ∞ $r→ ∞ $ . Under the assumption that f is supercritical for small u > 0 $u>0$ and is subcritical for large u > 0 $u>0$ , we show the existence of various types of solutions. The Pohozaev identity plays a crucial role in our investigation.