The caustic mathematician Roger Casals Gutiérrez saw on his kitchen wall in 2023. Caustics are a type of singularity, a mathematical phenomenon that occurs when an surface goes through a transition.

Consider F ∈ C(ℝ × X, Y) such that F(λ, 0) = 0 for all λ ∈ ℝ, where X and Y are Banach spaces. Bifurcation from the line ℝ × {0} of trivial solutions is investigated in cases where F(λ, ·) need not be ...

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In this paper we consider a class of singular two-point boundary value problem: (xαu')' = f(x, u), u(0) = A, u(1) = B, 0 < α < 1. The asymptotic expression of the spline finite difference solution for ...

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