In this paper, existence of solutions of third-order differential equation y′″（t）=f（t,y（t）,y′（t）,y″（t））with nonlinear three-point boundary condition{g（y（a）,y′（a）,y″（a））=0, h（y（b）,y′（b））=...In this paper, existence of solutions of third-order differential equation y′″（t）=f（t,y（t）,y′（t）,y″（t））with nonlinear three-point boundary condition{g（y（a）,y′（a）,y″（a））=0, h（y（b）,y′（b））=0, I（y（c）,y′（c）,y″（c））=0is obtained by embedding Leray-Schauder degree theory in upper and lower solutions method,where a, b, c∈ R,a〈 b〈 c; f ： [a,c]×R^3→R,g：R^3→R,h：R^2→R and I：R^3→R are continuous functions. The existence result is obtained by defining the suitable upper and lower solutions and introducing an appropriate auxiliary boundary value problem. As an application, an example with an explicit solution is given to demonstrate the validity of the results in this paper.展开更多
基金Foundation item： the Natural Science Foundation of Fujian Province （No. S0650010）.
文摘In this paper, existence of solutions of third-order differential equation y′″（t）=f（t,y（t）,y′（t）,y″（t））with nonlinear three-point boundary condition{g（y（a）,y′（a）,y″（a））=0, h（y（b）,y′（b））=0, I（y（c）,y′（c）,y″（c））=0is obtained by embedding Leray-Schauder degree theory in upper and lower solutions method,where a, b, c∈ R,a〈 b〈 c; f ： [a,c]×R^3→R,g：R^3→R,h：R^2→R and I：R^3→R are continuous functions. The existence result is obtained by defining the suitable upper and lower solutions and introducing an appropriate auxiliary boundary value problem. As an application, an example with an explicit solution is given to demonstrate the validity of the results in this paper.
