The Existence of Iterative Solutions for the One-Dimensional$P$-Laplacian
具$p$-Laplacian 算子的多点边值问题迭代解的存在性

In the paper, we get the maximal and minimal solutions of the following problem $$\left\{\begin{array}{l} ({\it {\it \Phi}}_{p}(u'))'+f(t,u,Tu)=0,~~~~0\leq{t}\leq{1},\\ u(0)=\d\sum \limits _{i=1}^{q-1}\gamma _i u(\delta_i),~~u(1)=\d\sum \limits _{i=1}^{m-1}\eta _i u(\xi_i), \end{array} \right. $$ where ${\it {\it \Phi}}_{p}(s)=|s|^{p-2}s,p>1$ ; $ 0<\delta_i<1,$$\gamma _i>0 \textrm{for}1\leq i\leq q-1 $; $ 0<\xi_{i}<1,$$\eta_{i}\geq0\textrm{for}1\leq i\leq m-1 $ and $ \sum\limits_{i=1}^{q-1}\gamma _i<1,$ $ \sum \limits_{i=1}^{m-1}\eta_i\leq1;$\ $ Tu(t)=\int_{0}^{t}k(t,s)u(s){\rm d}s,k(t,s)\in C(I\times I,R^+).$ The monotone iterative technique and an extension of Mawhin's continuation theorem are used in the paper.