The Sobolev-Kondrachov embedding and compactness theorems are extended to cover general unbounded domains, by introducing appropriate weighted Lp norms. These results are then applied to the Dirichlet ...

In this paper we will prove the coexistence of unbounded solutions and periodic solutions for the asymmetric oscillator $\ddot{x}+f(\dot{x})+ax^{+}-bx^{-}=\varphi (t,x)$, where a and b are positive ...