On the Structure of the Solution Set of u″ = f(t,u), u(0) = u(1) = 0 |
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Authors: | Gerd Herzog Roland Lemmert |
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Abstract: | The solution set of a Dirichlet problem x″ = f(t, x), x(0) = x(1) = 0, on a Banach space E and with f satisfying a Lipschitz condition, is homeomorphic to a closed subset of E. We prove that to an closed subset C of E there is a function f with Lipschitz constant arbitrarily close to π2, such that the solution set of the corresponding Dirichlet problem is homeomorphic to C. |
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Keywords: | Dirichlet BVP solution set topological structure |
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