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This paper is concerned with the nonlinear Schrödingerequation 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 boundedfrom below and satisfies V(x)→∞ as |x|→∞. From variational calculus  and acompactness lemma, the existence of standing waves and theirorbital stability are obtained

Orbital stability of standing waves for a class of Schrödinger equations with unbounded potential