Green's function for a third-order generalized right focal problem

Abstract We determine the Green's function for the third-order three-point generalized right focal boundary value problem x‴(t)=0, t 1 ⩽t⩽t 3 , x(t 1 )=x′(t 2 )=0, γx(t 3 )+δx″(t 3 )=0, where δ>0, and determine conditions on the coefficients and boundary points to ensure its positivity. Then we use the Krasnoselskii and Leggett and Williams fixed point theorems to prove the existence of solutions to the nonlinear problem x‴(t)=f t,x(t) , t 1 ⩽t⩽t 3 , x(t 1 )=x′(t 2 )=0, γx(t 3 )+δx″(t 3 )=0, for certain constraints placed on nonnegative f.

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