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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 α and also in the case when α(t)=tOpen image in new window, t∈[0,1]Open image in new window. In all cases, the argument β can change the character on [0,1]Open image in new window, see problem (1). It means that β can be delayed in some set J¯⊂[0,1]Open image in new window and advanced in [0,1]∖J¯Open image in new window. An example is added to illustrate the results.

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