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On a Class of Functional Differential Equations with Symmetries

1
Mathematical Institute of Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, Slovakia
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Department of Mathematical Analysis and Numerical Mathematics, Comenius University, Mlynská dolina, 842 48 Bratislava, Slovakia
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Institute of Mathematics, Czech Academy of Sciences, Brno branch, Žižkova 22, 616 62 Brno, Czech Republic
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Institute of Mathematics, Brno University of Technology, FBM, Kolejní 4, 612 00 Brno, Czech Republic
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(12), 1456; https://doi.org/10.3390/sym11121456
Received: 17 October 2019 / Revised: 20 November 2019 / Accepted: 22 November 2019 / Published: 27 November 2019
(This article belongs to the Special Issue Nonlinear Oscillations and Boundary Value Problems)
It is shown that a class of symmetric solutions of scalar non-linear functional differential equations can be investigated by using the theory of boundary value problems. We reduce the question to a two-point boundary value problem on a bounded interval and present several conditions ensuring the existence of a unique symmetric solution. View Full-Text
Keywords: functional differential equation; argument deviation; periodic; antiperiodic; symmetry; two-point problem; unique solvability functional differential equation; argument deviation; periodic; antiperiodic; symmetry; two-point problem; unique solvability
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Dilna, N.; Fečkan, M.; Rontó, A. On a Class of Functional Differential Equations with Symmetries. Symmetry 2019, 11, 1456.

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