Positive solutions of nonlocal singular boundary value problems

The paper presents the existence result for positive solutions of the differential equation (g(x))″ = f(t, x, (g(x))′) satisfying the nonlocal boundary conditions x(0) = x(T), min{x(t): t ∈ J} = 0. Here the positive function f satisfies local Carathéodory conditions on [0, T] × (0, ∞) × (ℝ\{0}) and f may be singular at the value 0 of both its phase variables. Existence results are proved by Leray-Schauder degree theory and Vitali's convergence theorem.