On contrast structures that arise when the type of stability of a root of a degenerate equation changes (Q1571160)

A boundary value problem for the singular quasilinear second-order equation \[ \varepsilon y''=(y'+1)[y-\gamma{(x)}], \] \[ y(0,\varepsilon)=y^0,\;y(1,\varepsilon)=y^1,\;y^0>\gamma{(0)},\;y'<\gamma{(1)}, \] is considered. It is established that, under certain conditions, a solution to such problem exists and has, in the limit as the perturbation parameter \(\varepsilon\) tends to zero, one or several corner points.