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- W2963977320 endingPage "5102" @default.
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- W2963977320 abstract "In this paper, the classical solution set (λ,u) of the one-dimensional prescribed mean curvature equation (⋆)−(u′1+(u′)2)′=λ(1−u)2,−L<x<L;u(−L)=u(L)=0, 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 (⋆) splits into two parts. In contrast, the solution set of the semilinear version of problem (⋆) is independent of L and exhibits only a saddle node bifurcation. Therefore, as this analysis suggests, the splitting bifurcation is a byproduct of the mean curvature operator coupled with the singular forcing." @default.
- W2963977320 created "2019-07-30" @default.
- W2963977320 creator A5047866756 @default.
- W2963977320 creator A5068447217 @default.
- W2963977320 date "2012-09-01" @default.
- W2963977320 modified "2023-10-16" @default.
- W2963977320 title "Analysis of a one-dimensional prescribed mean curvature equation with singular nonlinearity" @default.
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- W2963977320 doi "https://doi.org/10.1016/j.na.2012.04.025" @default.
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