Positive Solutions of Singular Initial-Boundary Value Problems to Second-Order Functional Differential Equations. (26th August 2008) - Jin, Fengfei; Yan, Baoqiang
Abstract : Positive solutions to the singular initial-boundary value problemsx _ _ = − f ( t, x t ), 0 < t < 1, x 0 = 0, x ( 1 ) = 0, are obtained by applying the Schauder fixed-point theorem, wherex t ( u ) = x ( t + u ) ( 0 ≤ t ≤ 1 ) on[ − r, 0 ] andf ( ⋅, ⋅ ) : ( 0, 1 ) × ( C + 0 ) → R + ( C + = x ∈ C ( [ − r, 0 ], R ), x ( t ) ≥ 0, ∀ t ∈ [ − r, 0 ] ) may be singular atφ ( u ) = 0 ( − r ≤ u ≤ 0 ) andt = 0 . As an application, an example is given to demonstrate our result.