Positive Solutions for a Class of Semipositone Problems

Here we consider the autonomous two point boundary value problem: −u (x) = λf(u(x)) ; x in (−1, 1), u(−1) = 0 = u(1), where λ 0 and f : [0,∞) rightarrow R is monotonically increasing and concave (f 0) with f(0) 0 (semipositone), f(t) 0 for some t 0. We obtain the exact number of positive solutions.