In this paper we consider the following Schrödinger equation: where V is a periodic continuous real function with 0 in a gap of the spectrum σ (A), A := -∆ + V and the classical Ambrosetti-Rabinowitz superlinear condition on g is replaced by a general super-quadratic condition.
Uniqueness and nondegeneracy of the ground state for a quasilinear Schrödinger equation with a small parameter
✍ Scribed by Alessandro Selvitella
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 223 KB
- Volume
- 74
- Category
- Article
- ISSN
- 0362-546X
No coin nor oath required. For personal study only.
✦ Synopsis
We study least energy solutions of a quasilinear Schrödinger equation with a small parameter. We prove that the ground state is nondegenerate and unique up to translations and phase shifts using bifurcation theory.
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