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.

Authors
Publisher
EDP Sciences
Number of issue
6
Language
English
Pages
226-239
Status
Published
Volume
12
Year
2017
Organizations
  • 1 RUDN University, Moscow, Russian Federation
Keywords
Elliptic problems; Functional differential equations with contracted arguments; Incommensurable contractions
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/5662/