We consider boundary value problems for scalar differential equation , , , where is a seventh-degree polynomial and is a parameter. We use the phase plane method combined with evaluations of time-map functions and make conclusions on the number of positive solutions. Bifurcation diagrams are constructed and examples are considered illustrating the bifurcation processes.
A. Kirichuka. F. Sadyrbaev. "Multiple Positive Solutions for the Dirichlet Boundary Value Problems by Phase Plane Analysis." Abstr. Appl. Anal. 2015 1 - 6, 2015. https://doi.org/10.1155/2015/302185