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arXiv · 1104.2139

Regularity and decay of solutions of nonlinear harmonic oscillators

Marco Cappiello·Fabio Nicola
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Abstract

We prove sharp analytic regularity and decay at infinity of solutions of variable coefficients nonlinear harmonic oscillators. Namely, we show holomorphic extension to a sector in the complex domain, with a corresponding Gaussian decay, according to the basic properties of the Hermite functions in R^d. Our results apply, in particular, to nonlinear eigenvalue problems for the harmonic oscillator associated to a real-analytic scattering, or asymptotically conic, metric in R^d, as well as to certain perturbations of the classical harmonic oscillator.

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Marco Cappiello, Fabio Nicola. 2011-04-12. Regularity and decay of solutions of nonlinear harmonic oscillators. https://arxiv.org/abs/1104.2139

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