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Results of Ambrosetti-Prodi type for non-selfadjoint elliptic operators
Boyan Sirakov, Carlos Tomei, André Zaccur
The well-known Ambrosetti-Prodi theorem considers perturbations of the Dirichlet Laplacian by a nonlinear function whose derivative jumps over the principal eigenvalue of the opera…
Global folds between Banach spaces as perturbations
Marta Calanchi, Carlos Tomei, André Zaccur
Global folds between Banach spaces are obtained from a simple geometric construction: a Fredholm operator of index zero with one dimensional kernel is perturbed by a compatible…
Abundance of cusps and a converse to the Ambrosetti-Prodi theorem
Marta Calanchi, Carlos Tomei, André Zaccur
According to the Ambrosetti-Prodi theorem, the map between appropriate functional spaces is a global fold. Among the hypotheses, the convexity of the function $…
Fibers and global geometry of functions
Marta Calanchi, Carlos Tomei, Andre Zaccur
Since the seminal work of Ambrosetti and Prodi, the study of global folds was enriched by geometric concepts and extensions accomodating new examples. We present the advantages of…
Geometric Aspects of Ambrosetti-Prodi operators with Lipschitz nonlinearities
Carlos Tomei, André Zaccur
For Dirichlet boundary conditions on a bounded domain, what happens to the critical set of the Ambrosetti-Prodi operator if the nonlinearity is only a Lipschitz map? It turns out t…