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

[摘要] We determine the Green's function for the third-order three-point generalized right focal boundary value problem x'''(t) = 0, t(1) less than or equal to t less than or equal to t(3), x(t(1)) = x'(t(2)) = 0, gammax(t(3)) + deltax(t(3)) = 0, where delta > 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) less than or equal to t less than or equal to t(3), x(t(1)) = x'(t(2)) = 0, gammax(t(3)) + deltax (t(3)) = 0, for certain constraints placed on nonnegative f. (C) 2003 Published by Elsevier Inc.

[发布日期] 2003-12-01

[关键词] differential equations;boundary value problem;Green's function;third order;right focal