Symmetric nonlinear functional differential equations at resonance

Abstract

It is shown that a class of symmetric solutions of the scalar nonlinear functional differential equations at resonance with deviations from $\mathbb{R}\to\mathbb{R}$ can be investigated by using the theory of boundary-value problems. Conditions on a solvability and unique solvability are established. Examples are presented to illustrate given results.

Keywords

• symmetric solution
• solvability
• lyapunov–schmidt reduction method