On nonlinear boundary conditions satisfying certain asymptotic behavior

In this paper we consider a second-order boundary value problem of the form y″(t)=−λa(t)g(y(t))y″(t)=−λa(t)g(y(t)), y(0)=φ(y)y(0)=φ(y), y(1)=0y(1)=0. We demonstrate that if the nonlinear functional φ(y)φ(y) satisfies certain asymptotic behavior, then the problem will possess at least one positive solution. These results generalize and improve on some recent results in the literature on boundary value problems with nonlocal, nonlinear boundary conditions, and we provide some examples, which illustrate these generalizations and improvements.