V knige izuchayutsya differentsial'nye uravneniya vtorogo poryadka, dopuskayushchie negladkie, a takzhe razryvnye resheniya. Ustanavlivayutsya polnye analogi klassicheskikh ostsillyatsionnykh rezul'tatov Shturma (chislo nuley, ikh peremezhaemost' dlya sobstvennykh funktsiy). V osnove analiza lezhit utochnenie integrala Stilt'esa. Za schet rasshireniya ponyatiya integrala udaetsya sokhranit' potochechnoe tolkovanie kak resheniy, tak i sootnosheniy, chto v ramkakh teorii obobshchennykh funktsiy bylo by nevozmozhno.