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È stabilito un teorema di confronto per una classe di punti focali di una non autoaggiunta equazione differenziale di ordine pari. È dato un semplice esempio secondo il quale il detto criterio non può essere esteso a punti coniugati.
L'identità di Picone è uno strumento fondamentale nello studio del comportamento oscillatorio delle soluzioni delle equazioni differenziali Sturm-Liouville. Essa è strettamente collegata alla condizione di Legendre nel calcolo delle variazioni. Nella Nota presente si dimostra che un'analoga identità per le equazioni lineari differenziali ordinarie del quart'ordine è collegata pur essa al calcolo delle variazioni.
Nella Nota presente sono dati limiti superiori per la mutua distanza di due punti coniugati consecutivi competenti ad un'equazione differenziale ordinaria del quarto ordine non autoaggiunta.
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