His work on the integration of partial differential equations and a search to determine maxima and minima using variational methods brought him close to the investigations which Lie was carrying out around the same time.
Kanyang trabaho sa integration ng mga bahagi ng kaugalian ng isang equation at paghahanap upang matukoy maxima at minima gamit variational pamamaraan na nagdala sa kanya upang isara ang mga pagsisiyasat na humiga / magsinungaling ay ang pagdala sa paligid ng parehong oras.