Analysis of a one-dimensional prescribed mean curvature equation with singular nonlinearity
ND Brubaker, JA Pelesko - Nonlinear Analysis: Theory, Methods & …, 2012 - Elsevier
In this paper, the classical solution set (λ, u) of the one-dimensional prescribed mean
curvature equation for λ> 0 and L> 0, is analyzed via a time map. It is shown that the solution
set depends on both parameters λ and L and undergoes two bifurcations. The first is a
standard saddle node bifurcation, which happens for all L at λ= λ∗(L). The second is a
splitting bifurcation, namely, there exists a value L∗ such that as L transitions from greater
than or equal to L∗ to less than L∗ the upper branch of the bifurcation diagram of problem …
curvature equation for λ> 0 and L> 0, is analyzed via a time map. It is shown that the solution
set depends on both parameters λ and L and undergoes two bifurcations. The first is a
standard saddle node bifurcation, which happens for all L at λ= λ∗(L). The second is a
splitting bifurcation, namely, there exists a value L∗ such that as L transitions from greater
than or equal to L∗ to less than L∗ the upper branch of the bifurcation diagram of problem …
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