... two-pointBVPs.Motivated by the work above, in this paper we will extend the results of 4, 19 , 22–24 to problem 1.3. On the other hand, it is also interesting and important to discuss the existence of positive ... ∞.3.36Then, conditions H3 and H4 of Theorem 3.1 hold. Hence, by Theorem 3.1 ,the conclusion follows, and the proof is complete.AcknowledgmentThis work is supported by the National ... 0,m−2i1βiξm−1i< 1. Furthermore, they obtained the existence of positive solutions by means of fixed point index theory.Recently, Yang and Wei 23 and the author of 24 improved and generalized the results...