After proposing a variant of the Poincaré–Bohl theorem, we extend the Poincaré– Miranda theorem in several directions, by introducing an avoiding cones condition. We are thus able to deal with functions defined on various types of convex domains, and situations where the topological degree may be different from ±1. An illustrative application is provided for the study of functionals having degenerate multi-saddle points.
Generalizing the Poincaré–Miranda theorem: the avoiding cones condition
FONDA, ALESSANDRO;GIDONI, PAOLO
2016-01-01
Abstract
After proposing a variant of the Poincaré–Bohl theorem, we extend the Poincaré– Miranda theorem in several directions, by introducing an avoiding cones condition. We are thus able to deal with functions defined on various types of convex domains, and situations where the topological degree may be different from ±1. An illustrative application is provided for the study of functionals having degenerate multi-saddle points.File in questo prodotto:
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