Positive solutions of fourth-order nonlinear singular Sturm-Liouville eigenvalue problems
Positive solutions of fourth-order nonlinear singular Sturm-Liouville eigenvalue problems
复制标题
DOI：
10.1016/j.jmaa.2006.03.029
复制
发表时间：
2007-02
影响因子：
1.3
通讯作者：
Lishan Liu;Xinguang Zhang;Yonghong Wu
中科院分区：
文献类型：
--
作者：
Lishan Liu;Xinguang Zhang;Yonghong Wu
本文考虑如下四阶奇异Sturm-Liouville特征值问题正解的存在性，其中λ>0，g，p在t=0和/或1处可以是奇异的.此外，F（t，x，y）也可以在x=0和/或y=0处具有奇点。利用锥上的不动点理论，得到了λ的一个显式区间，使得对于该区间内的任意λ，保证了边值问题至少存在一个正解.我们的结果推广和改进了许多已知的结果，包括奇异和非奇异的情况。
We consider the existence of positive solutions for the following fourth-order singular Sturm–Liouville eigenvalue problems where λ>0, g,p may be singular at t=0 and/or 1. Moreover, F(t,x,y) may also have singularity at x=0 and/or y=0. By using fixed point theory in cones, an explicit interval for λ is derived such that for any λ in this interval, the existence of at least one positive solution to the boundary value problem is guaranteed. Our results extend and improve many known results including singular and nonsingular cases.