On the Existence of a Positive Solution of a Boundary Value Problem for a Nonlinear Second-Order Functional-Differential Equation with Integral Boundary Conditions

A boundary value problem for a nonlinear second-order functional-differential equation on the interval \([0,1]\) with integral boundary conditions is considered. Sufficient conditions for the existence of at least one positive solution of the problem under consideration are found by using special topological tools. A nontrivial example in which the sufficient conditions for the unique solvability of the problem are satisfied is given.