TY - JOUR T1 - A Hardy Type Inequality and Inde Nite Eigenvalue Problems on the Homogeneous Group JO - Journal of Partial Differential Equations VL - 4 SP - 28 EP - 38 PY - 2002 DA - 2002/11 SN - 15 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5459.html KW - Hardy type inequality KW - Picone type identity KW - indefinite eigenvalue problem KW - homogeneous group AB - In this paper we present a Hardy type inequality and a Picone type identity for the real sub-Laplacian on the homogeneous group. The existence of the indefinite eigenvalue problem and the simplicity of the principal eigenvalue are proved.