On the Existence of the Fundamental Eigenvalue of an Elliptic Problem in R^N

TL;DR

This paper investigates conditions for the existence of the fundamental eigenvalue in an elliptic problem in R^N, with applications to stability analysis of nonlinear Schrödinger equation standing waves.

Contribution

It provides new sufficient conditions for the existence of the fundamental eigenvalue in elliptic problems in R^N.

Findings

Established sufficient conditions for eigenvalue existence

Linked eigenvalue results to stability of nonlinear Schrödinger standing waves

Enhanced understanding of spectral properties in unbounded domains

Abstract

We study an eigenvalue problem for functions in R^N and we find sufficient conditions for the existence of the fundamental eigenvalue. This result can be applied to the study of the orbital stability of the standing waves of the nonlinear Schroedinger equation.