Mexanika, fizika, biologiya, iqtisod va boshqa fanlar masalalari nochiziqli tenglamalarga yoki ularning sistemalariga keltiriladi. Bunday tenglamalarni yechimlari regulyar va singulyar yechimlarga bo‘linadi. Regulyar yechim yaqinida oshkormas funksiya haqidagi teorema yoki uning analogi qo‘llaniladi, u boshqa barcha yaqin yechimlarning tavfsifini beradi. Singulyar yechim yaqinida oshkormas funksiya haqidagi teoremani qo‘llab bo‘lmaydi. Ushbu ishda Darajali gometriyaning asosiy konsepsiyasi unga kiruvchi monom darajalari ko‘rsatkichlari bo‘yicha tenglamalar yechimlari xossalarini o‘rganish hisoblanadi.
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