cases

Equilibria

$h>h^{\ast }>c>0$

None

$h=h^{\ast }>0$

$E_{SN}=\left(x_{SN},0\right)=\left(\frac{1-c}{2},0\right)$

$h^{\ast }>h>c>0$

$E_1=\left(x_1,0\right)=\left(\frac{1-c-\sqrt{\Delta }}{2},0\right)$ and $E_2=\left(x_2,0\right)=\left(\frac{1-c+\sqrt{\Delta }}{2},0\right)$

$h^{\ast }>c=h>0$

$E_2=\left(x_2,0\right)=\left(1-c,0\right)$

$h^{\ast }>c>h>0$

$E_2=\left(x_2,0\right)=\left(\frac{1-c+\sqrt{\Delta }}{2},0\right)$