A multiplicity result of positive solutions for third-order multi-point boundary value problem
Consider the boundary value problem NEWLINE\[NEWLINE\begin{gathered} x'''(t)= f(t,x(t), x'(t), x''(t))\quad\text{for }t\in (0,1),\\ x''(1)= 0,\;x'(1)= 0,\;x(0)= \sum^{m-2}_{i=1} \beta_i x(\xi_i),\end{gathered}\tag{\(*\)}NEWLINE\]NEWLINE where \(0<\xi_1<\xi_2<\cdots< \xi_{m-2}< 1\), \(0<\beta_i< 1\) for \(1\leq i\leq m-2\), \(\sum^{m-2}_{i=1} \beta_i< 1\), \(f\in C((0,1)\times \mathbb{R}^3,[0,+ \infty))\).NEWLINENEWLINE The authors use the fixed point theorem due to Avery and Peterson to establish the existence of at least three positive solutions to \((*)\).
scientific article; zbMATH DE number 6200646