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

Guanggan Chen, Jian Zhang and Yunyun Wei

International Journal of Stochastic Analysis, 2006, vol. 2006, 1-7

Abstract:

This paper is concerned with the nonlinear Schrödinger equation with an unbounded potential i ϕ t = − Δ ϕ + V ( x ) ϕ − μ | ϕ | p − 1 ϕ − λ | ϕ | q − 1 ϕ , x ∈ ℝ N , 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.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:057676

DOI: 10.1155/JAMSA/2006/57676

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