ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

The Notion of Ellipticity for Nonlinear Second Order Differential Equations

Author(s):

Svetlana Ivanovna Prokofyeva

The St. Petersburg State University of Architecture and Civil Engineering,
math. dept. Assoc.Prof. PhD

svetlanaprokof@yandex.ru

Galina Vladimirovna Yakunina

The St. Petersburg State University of Architecture and Civil Engineering,
math. dept. Assoc.Prof. PhD

yakuninagalina@yandex.ru

Abstract:

The article reconsiders the role of ellipticity notion for nonlinear differential second order equations. It demonstrates that the positive monotone cone is a natural set of solvability and uniqueness of the solution of Dirichlet problem for these equations. The article gives the example of equations that are elliptic in the cone as well as out of the cone. This equation has a solution both in the cone and out of the cone. These solutions are different.

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