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 < t < 1, together with the boundary conditions u(0) = u′ (p) = u″ (1) = 0, where λ > 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 sharp
Graef, J. R., & Yang, B. O. (2006). Positive solutions of a nonlinear third order Eigenvalue problem. Dynamic Systems and Applications, 15(1), 97-110.