非线性四阶两点边值问题解的存在性

Existence of solutions to nonlinear fourth-order two-point boundary-value problems

讨论含有两个参数的非线性常微分方程四阶两点边值问题u′′′′(t)+λ(αu(t)-βu″(t))+g(t,u′(t),u″(t))=h(t),t∈(0,1);u(0)=u(1)=u″(0)=u″(1)=0解的存在性,这里λ∈R,g:[0,1]×R2→R为连续函数,h∈L1(0,1),参数α,β满足条件(C1)(α,β)∈(0,+∞)×(0,+∞).

The existence of solutions to the nonlinear fourth-order two-point boundary-value problem defined by following ordinary differential equation with two parameters u′′′′（t）＋λ（au（t）-βu″（t））＋g（t,u′（t）,u″（t））=h（t）,t∈（0,1）;u（0）=u（1）=u″（0）=u″（1）=0 was discussed, where ,λ∈R,g：[0,1]×R2→R is continuous function, h∈ L1 （0,1）, and parameters a and β satisfy condition（C1 ） ;（α,β）∈（0,＋∞）×（0,＋∞）.