Singular third-order boundary value problems (Q1177310)

The author considers third-order boundary value problems \(y'''+f(t,y,y',y'')=0,\;0<t<1\), where the functions \(y\) satisfy certain boundary conditions, e.g., \(y''(1)=c\geq 0\), \(y'(0)=b\geq0\), \(y(0)=a\geq0\). The function \(f\) is singular at \(t=0\), \(t=1\), \(y=0\), \(y'=0\), and/or \(y''=0\). In three sections, the three particular cases \(f(t,y)\), \(f(t,y,y')\), and \(f(t,y,y'')\) are treated. For these functions \(f\), various subcases are considered, for which the existence of solutions is shown. Some examples to which the derived general results apply are considered.