摘要:
In this paper,we investigate the existence of positive solutions for the following fourth-order Sturm-Liouville boundary value problem with p-Laplacian operator:{(Φp(u″(t)))″+q(t)f(t,u(t),u″(t))=0,t∈(0,1), αu(0)-βu′(0)=0,γu(1)+δu′(1)=0,u″(0)=0,u′″(0)=0, w here Φp(s)=∣s∣p-2 s,p >1;f:[0,1]×[0,+∞)×R→[0,+∞) is continuous;q(t)> 0,t ∈(0,1).%本文运用迭代法研究了带 p-Laplacian算子的四阶Sturm-Liouville边值问题{(Φp(u″(t)))″+q(t)f(t,u(t),u″(t))=0,t∈(0,1), αu(0)-βu′(0)=0,γu(1)+δu′(1)=0,u″(0)=0,u′″(0)=0正解的存在性,其中Φp(s)=∣s∣p-2 s,p >1;f:[0,1]×[0,+∞)×R→[0,+∞]连续;q(t)>0,t ∈(0,1).