Global bifurcation diagrams of one node solutions in a class of degenerate boundary value problems

Figure 1.  The weight function $a=a_{0}$

Figure 2.  The weight function $a=a_\varepsilon $ for $\varepsilon >0$

Figure 3.  The metasolution $\boldsymbol{\mathfrak{m}}_{[(\frac{\pi}{h})^2, 1, 0]}$ for $a=a_{0}$

Figure 4.  A solution $u_{[{\rm{\lambda }}, 1, 0]}\sim \boldsymbol{\mathfrak{m}}_{[(\frac{\pi}{h})^2, 1, 0]}$

Figure 5.  The global bifurcation diagram for $\varepsilon=0.1$ and $0\leq {\rm{\lambda }} \leq 60$

Figure 6.  A series of solution plots on the principal curve for $\pi^2 < {\rm{\lambda }} < 400$ (left) and $450 < {\rm{\lambda }} < 700$ (right)

Figure 7.  A series of solutions on the isola for $20 < {\rm{\lambda }} < 40$

Figure 8.  A series of solutions on the isola for $70 < {\rm{\lambda }} < 140$

Figure 9.  The zeroes of the solutions computed for ${\rm{\lambda }}\leq 180$

Figure 10.  A zoom of the bifurcation diagram for $\varepsilon=0.001$

Figure 11.  Two significant components of the bifurcation diagram

Figure 12.  Two magnifications of the bifurcation diagram

Figure 13.  The zeroes of the solutions computed for $\varepsilon=0.0037$

Figure 14.  Two significant magnifications of the zeroes plots

Figure 15.  A series of solution plots along $\mathfrak{C}_2^+$

Figure 16.  A series of solution plots along ${\mathfrak{J}}^+$

Figure 17.  Solution plots along $\mathfrak{C}_2^+$

Figure 18.  Crossing the turning point of ${\mathfrak{J}}^+$

Figure 19.  Two components of the bifurcation diagram for $\varepsilon=0.0036$

Figure 20.  The two components plotted in Figure 19

Figure 21.  The zeroes of the solutions computed for $\varepsilon=0.0036$

Figure 22.  Two significant magnifications of the zeroes plots