Tyagi, J.J.Tyagi2025-08-302025-08-302013-06-0110.1016/j.aml.2012.12.0202-s2.0-84875237533http://repository.iitgn.ac.in/handle/IITG2025/21157The purpose of this note is to show a generalization to Picone's identity in a nonlinear framework. The classical Picone's identity turns out to be a particular case of our result. We show, as an application of our results, that the Morse index of the zero solution to a semilinear elliptic boundary value problem is 0 and also establish a linear relationship between the components of the solution of a nonlinear elliptic system. © 2012 Elsevier Ltd. All rights reserved.trueBoundary value problems for second-order elliptic systems | Semilinear elliptic equationsArticle624-626June 201320arJournal13