一类完全四阶边值问题解的存在性

Existence of solutions for a class of fully fourth-order boundary value problems

讨论完全四阶两点边值问题{u(4)(t)=f(t,u(t),u′(t),u′′(t),u′′′(t)),t∈[0,1],u(0)=u(1)=u′′(0)=u′′(1)=0解的存在性,其中f:[0,1]×R4→R为连续函数。在不限制非线性项的增长条件,也不假定非负的一般情形下,f(t,x0,x1,x2,x3)关于x3满足Nagumo型条件时,运用截断函数技巧和上下解方法讨论了该问题解的存在性。

In this paper,the existence of solutions for a class of fully fourth-order boundary value problem{u(4)(t)=f(t,u(t),u′(t),u′′(t),u′′′(t)),t∈[0,1]u(0)=u(1)=u′′(0)=u′′(1)=0 is discussed,where f:[0,1]×R4→R is a continuous function.Without restricting the growth condition of nonlinear terms and without assuming that they are non-negative in the general case,when f(t,x0,x1,x2,x3)satisfies the proper Nagumo-type condition on x3,we obtain the existence of solutions for this equation via a truncating function and the lower and upper solution method.