Existence of positive solutions for second-order boundary value problem with one parameter

In the case of not requiring f (t,u) to be nonnegative, by transforming the boundary value problem into the integral equation system, and applying the fixed point index theory, the author studies the following second-order boundary value problem with one parameter −u +λu = f (t,u), 0 < t <1, u(0) = u(1) = 0, and obtains the results on the existence of its positive solution. © 2006 Elsevier Inc. All rights reserved.