Math. Model. Nat. Phenom.
Volume 12, Number 6, 2017Special Issue - Nonlocal and delay equations
|Page(s)||226 - 239|
|Published online||30 December 2017|
Elliptic functional differential equations with incommensurable contractions
Accepted: 13 November 2017
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.
Mathematics Subject Classification: 35J15 / 35J25
Key words: Functional differential equations with contracted arguments / elliptic problems / incommensurable contractions
© EDP Sciences, 2017
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