Abstract
This paper is concerned with the nonlinear Schrödinger
equation with an unbounded potential iϕt=−Δϕ+V(x)ϕ−μ|ϕ|p−1ϕ−λ|ϕ|q−1ϕ, x∈ℝN, t≥0, where μ>0, λ>0, and 1<p<q<1+4/N. The potential V(x) is bounded
from below and satisfies V(x)→∞ as |x|→∞. From variational calculus and a
compactness lemma, the existence of standing waves and their
orbital stability are obtained.