Positive solutions to second-order differential equations with dependence on the first-order derivative and nonlocal boundary conditions

In this paper, we consider the existence of positive solutions for second-order differential equations with deviating arguments and nonlocal boundary conditions. By the fixed point theorem due to Avery and Peterson, we provide sufficient conditions under which such boundary value problems have at least three positive solutions. We discuss our problem both for delayed and advanced arguments alpha and also in the case when alpha(t) = t, t is an element of [0, 1]. In all cases, the argument beta can change the character on [0, 1], see problem (1). It means that beta can be delayed in some set and advanced in (J) over bar subset of [0, 1] \ (J) over bar. An example is added to illustrate the results.