Existence and iteration of positive solutions to third order three-point BVP with increasing homeomorphism and positive homomorphism (Q350781)

The authors study the existence of positive solutions and establish two iterative schemes for the nonlinear third-order three-point boundary value problem NEWLINE\[NEWLINE\begin{gathered}\phi(u'')'(t)+q(t)f(u(t))=0,\quad 0<t<1, \\ u(0)=-\beta u(\xi),\;u'(1)=0, \;\phi(u''(0))=\delta \phi(u''(\xi)), \end{gathered}NEWLINE\]NEWLINE where \(\phi:\mathbb{R}\to\mathbb{R}\) is an increasing and positive homeomorphism. The main tool is the monotone iterative technique.