Abstract
Let the function u satisfy Dirichlet boundary conditions on a bounded domain \( \Omega \). What happens to the critical set of the Ambrosetti–Prodi operator \( F(u)= -\Delta u-f(u) \). if the nonlinearity is only a Lipschitz map? It turns out that many properties which hold in the smooth case are preserved, despite of the fact that F is not even differentiable at some points. In particular, a global Lyapunov–Schmidt decomposition of great convenience for numerical solution of F(u) = g is still available.
Mathematics Subject Classification (2010). 35B32, 35J91, 65N30.
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Dedicated to Bernhard, with affection and admiration
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Tomei, C., Zaccur, A. (2014). Geometric Aspects of Ambrosetti–Prodi Operators with Lipschitz Nonlinearities. In: de Figueiredo, D., do Ó, J., Tomei, C. (eds) Analysis and Topology in Nonlinear Differential Equations. Progress in Nonlinear Differential Equations and Their Applications, vol 85. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-04214-5_26
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DOI: https://doi.org/10.1007/978-3-319-04214-5_26
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