Multi-peak bound states for Schrödinger equations with compactly supported or unbounded potentials
Multi-peak bound states for Schrödinger equations with compactly supported or unbounded potentials
In this paper, we will study the existence and qualitative property of standing waves \psi (x,t) = e^{−\frac{iEt}{\varepsilon }}u(x) for the nonlinear Schrödinger equation i\varepsilon \frac{\partial \psi }{\partial t} + \frac{\varepsilon ^{2}}{2m}\mathrm{\Delta }_{x}\psi −(V(x) + E)\psi + K(x)|\psi |^{p−1}\psi = 0 , (t,x) \in \mathbb{R}_{ + } \times \mathbb{R}^{N} . …