ABSTRACT
Throughout this paper, let C : = C [ − r , θ ] , r ⩾ 0 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003067498/6ba0c26b-f086-40cc-86ed-1693dc596221/content/eq4164.tif"/> , be the Banach space of continuous functions φ : [ − r , 0 ] → R n https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003067498/6ba0c26b-f086-40cc-86ed-1693dc596221/content/eq4165.tif"/> with the supnorm. For any continuous function z : R → R n https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003067498/6ba0c26b-f086-40cc-86ed-1693dc596221/content/eq4166.tif"/> and t ∈ R , z 1 ∈ C https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003067498/6ba0c26b-f086-40cc-86ed-1693dc596221/content/eq4167.tif"/> is defined by means of z l ( θ ) = z ( t + θ ) , − r ⩽ θ ⩽ 0 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003067498/6ba0c26b-f086-40cc-86ed-1693dc596221/content/eq4168.tif"/> . In this paper, we investigate the existence of homoclinic orbits for perturbed functional differential equations () z ′ ( t ) = g z l + h t , z t , ε , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003067498/6ba0c26b-f086-40cc-86ed-1693dc596221/content/eq4169.tif"/>
