Positive Solutions of a Nonlinear Third Order Eigenvalue Problem

The authors consider the boundary value problem consisting of the third order nonlinear ordinary differential equation u‴ (t) = λ g(t) f (u), 0 \u3c t \u3c 1, together with the boundary conditions u(0) = u′ (p) = u″ (1) = 0, where λ \u3e 0 is a parameter, and p ∈ (1/2, 1) is a constant. They give existence and nonexistence results for positive solutions of this problem. Examples are included to show that the results are shar