Elliptic functional differential equations with incommensurable contractions

The "commensurability" of transformations has been a crucial assumption in the study of solvability and regularity of solutions for elliptic functional differential equations in domains, while equations with incommensurable transformations are much less studied. In the paper, we consider an equation containing multiplicatively incommensurable contractions of the arguments of the unknown function in the principal part. Algebraic conditions for unique solvability of the Dirichlet problem will be obtained as well as conditions ensuring the existence of an infinite-dimensional null-space. The equation considered is an elliptic analog of the generalized pantograph equation studied by many authors. As a complementary conclusion, we observe that the spectral properties of functional operators with contractions are unstable with respect to small perturbations of scaling parameters. © EDP Sciences, 2017.

Авторы
Редакторы
-
Издательство
EDP Sciences
Номер выпуска
6
Язык
Английский
Страницы
226-239
Статус
Опубликовано
Подразделение
-
Номер
-
Том
12
Год
2017
Организации
  • 1 RUDN University, Moscow, Russian Federation
Ключевые слова
Elliptic problems; Functional differential equations with contracted arguments; Incommensurable contractions
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/5662/