The existence of multiple positive solutions to boundary value problems of nonlinear delay differential equations with countably many singularities on infinite interval

✍ Scribed by Yuming Wei; Patricia J.Y. Wong; Weigao Ge

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 612 KB
• Volume: 233
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2009.10.005

✦ Synopsis

In this paper, we consider the existence of countably many positive solutions to a boundary value problem of a nonlinear delay differential equation with countably many singularities on infinite interval

where φ : R → R is an increasing homeomorphism and a positive homomorphism with φ(0) = 0, x t is a function in C ([-r, 0], R) defined by x t (σ ) = x(t +σ ) for -r ≤ σ ≤ 0, and ξ ∈ C ([-r, 0], R). By using the fixed-point index theory and a new fixed-point theorem in a cone, we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem. The conclusions in this paper essentially extend and improve the known results.