一类完全三阶边值问题解的存在性

Existence of Solutions for a Class of FullyThird-Order Boundary Value Problem

用新的截断函数技巧与上下解方法,讨论完全三阶边值问题:u(t)=f(t,u(t),u′(t),u″(t)),t∈[0,1],u(0)=u′(1)=u″(1)=0解的存在性,其中f:[0,1]×ℝ3→ℝ连续.在非线性项f满足一些不等式的条件下给出该问题解的存在性.特别地,在不要求非线性项f非负的一般情形下得到了该问题正解的存在性.

Using the new truncation function technique and the met hod of upper and lower solutions,we discussed the existence of solutions for the fully third-order boundary value problem:u(t)=f(t,u(t),u′(t),u″(t)),t∈[0,1],u(0)=u′(1)=u″(1)=0,where f:[0,1]×ℝ3→ℝwas a continuous function.Under the condition that the nonlinear term f satisfied some inequaliti es,we gave the existence of solutions to the problem.In particular,we obtained the existence o f the positive solutions to the problem when the nonlinear term f was not required to be non-negative.