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arXiv · 1403.7762

A nonlinear eigenvalue problem arising in a nanostructured quantum dot

Abbasali Mohammadi·Fariba Bahrami
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Abstract

In this paper we investigate a minimization problem related to the principal eigenvalue of the $s$-wave Schr\"{o}dinger operator. The operator depends nonlinearly on the eigenparameter. We prove the existence of a solution for the optimization problem and the uniqueness will be addressed when the domain is a ball. The optimized solution can be applied to design new electronic and photonic devices based on the quantum dots.

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Abbasali Mohammadi, Fariba Bahrami. 2014-03-30. A nonlinear eigenvalue problem arising in a nanostructured quantum dot. https://doi.org/10.1016/j.cnsns.2013.11.017

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