Solvability of multi-point boundary value problem at resonance (III)

摘要

In this paper, we consider the following second-order ordinary differential equation(E)subject to one of the following boundary value conditions:(B1)(B2)(B3)(B4)where , β∈R, 0<ξ1<ξ2<⋯<ξm−2<1, 0<η<1. When all the αi's have no the same sign, some existence results are given for (E) with boundary conditions , , , at resonance case. We also give some examples to demonstrate our results.