含有p-Laplacian算子的四阶Sturm-Liouville边值问题迭代解的存在性

Existence and iteration of positive solutions for fourth-order Sturm-Liouville boundary value problems with p-Laplacian

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).

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）=,γu（1）＋δu＇（1）=0,u″（0）=0,u？（0）=0, where φ_p（s）=∣s∣^（p-2）s,p〉1;f：[0,1]×[0,＋∞）×R→[0,＋∞）连续;q（t）〉0,t∈（0,1）.