Abstract
We establish not only sufficient but also necessary conditions for existence of solutions to a singular multi-point third-order boundary value problem posed on the half-line. Our existence results are based on the Krasnosel'skii fixed point theorem on cone compression and expansion. Nonexistence results are proved under suitable a priori estimates. The nonlinearity f = f (t, x, y) which satisfies upper and lower-homogeneity conditions in the space variables x, y may be also singular at time t = 0. Two examples of applications are included to illustrate the existence theorems.