Convergence in a neutral delay differential equation

Abstract

By using some facts from limiting equations theory we prove that the solution x(.;ϕ), with continuous initial condition ϕ, of the neutral functional differential equation [x(t)-cx(t-r)]' =-F(x(t))+F(x(t-r)), t>0, where c ε [0,1), r≧0 and F is (not necessarily strictly) increasing. satisfies lim x(t;ϕ) = &, where & is the unique root of the algebraic equation [math001]

Keywords:

• Neutral equations
• equilibrium
• limiting functions

Keywords:

• 34K20
• 34K25
• 34C35