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

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,p1;f:0,1]×0,+∞)×R→0,+∞)连续;q(t)0,t∈(0,1).

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

In this paper,we investigate the existence of positive solutions for the following fourth-order Sturm-Liouville boundary value problem with $p$-Laplacian $$(\phi_{p}(u''(t)))''+q(t)f(t,u(t),u''(t))=0,\quad t\in (0,1),$$ $$\alpha u(0)-\beta u''(0)=0,\gamma u(1)+\delta u''(1)=0,u''(0)=0,u''(0)=0,$$ where~$\phi_{p}(s)=|s|^{p-2}s,~p>1;f:0,1]\times0,+\infty)\times R\rightarrow0,+\infty)$~is continuous;~$q(t)\geq0,t\in(0,1).$