Positive solutions of singular positone dirichlet boundary value problems

Abstract

The singular Dirichlet boundary value problem x″ + μ q( t) f( t,x,x′) = 0, x(0) = x( T) = 0 is considered. Here f( t,x,y) ≥ 0 may be singular at x = 0 and x = A > 0 of the phase variable x and at y = 0 of the phase variable y. Effective sufficient conditions imposed upon μ, q, and f are given for the solvability of the above problem in the set { x : x ∈ C 1( J) ∩ C 2((0, T) β t : t ∈ [0, T], x′( t) = 0}), 0 < x( t) < A, for t ∈ (0, T)}.