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Positive solutions for resonant and non-resonant nonlinear third-order multi-point boundary value problems
Chunfang Shen,Hui Zhou,Liu Yang
Keywords:M-point boundary value problem; Resonance; Positive solution; Cone; Fixed point
      Abstract In this paper, positive solutions for a kind of third-order multi-point boundary value problem under the resonant conditions are considered.By using Leggett-Williams norm-type theorem due to O''Regan and Zima, existence result of at least one positive solution is established. It is remarkable to point out that it is the first time that the positive solution is considered for third-order boundary value problem at resonance. Some examples are given to demonstrate the main results.