Data di Pubblicazione:
2020
Citazione:
Positive eigenvectors and simple nonlinear maps / M. Calanchi, C. Tomei. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - (2020). [Epub ahead of print] [10.1016/j.jfa.2020.108823]
Abstract:
For linear operators L,T and nonlinear maps P, we describe classes of simple maps F = I −PT, F = L−P between Banach and Hilbert spaces, for which no point has more than two preimages. The classes encompass known examples (homeomorphisms, global folds) and the weaker, geometric, hypotheses suggest new ones. The operator L may be the Laplacian with various boundary conditions, as in the original Ambrosetti-Prodi the- orem, or the operators associated with the quantum harmonic oscillator, the hydrogen atom, a spectral fractional Laplacian, elliptic operators in non-divergent form. The maps P include the Nemitskii map P(u) = f(u) but may be non-local, even non-variational. For self-adjoint operators L, we employ familiar results on the nondegeneracy of the ground state. On Banach spaces, we use a variation of the Krein-Rutman theorem.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Ambrosetti-Prodi theorem; folds; Krein-Rutman theorem; positivity preserving semigroups
Elenco autori:
M. Calanchi, C. Tomei
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