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

摘要:

文章运用迭代法研究了带p-Laplacian算子的四阶Sturm-Liouville边值问题 {p}(u''(t)))''+q(t)f(t,u(t),u''(t))=0,\quad t\in (0,1), u(0)-\beta u'(0)=0,\gamma u(1)+\delta u'(1)=0,u''(0)=0,u'''(0)=0 正解的存在性,~其中~$\phi_{p}(s)=|s|^{p-2}s,p>1;~f:[0,1]\times[0,+\infty)\times R\rightarrow[0,+\infty)$~连续;~$q(t)\geq0,t\in(0,1).

Abstract:

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~$\phi_{p}(s)=|s|^{p-2}s,~p>1;f:[0,1]\times[0,+\infty)\times R\rightarrow[0,+\infty)$~is continuous;~$q(t)\geq0,t\in(0,1).$